Properties

Label 8640.2.a
Level $8640$
Weight $2$
Character orbit 8640.a
Rep. character $\chi_{8640}(1,\cdot)$
Character field $\Q$
Dimension $128$
Newform subspaces $92$
Sturm bound $3456$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 8640 = 2^{6} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8640.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 92 \)
Sturm bound: \(3456\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8640))\).

Total New Old
Modular forms 1800 128 1672
Cusp forms 1657 128 1529
Eisenstein series 143 0 143

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(16\)
\(+\)\(+\)\(-\)\(-\)\(18\)
\(+\)\(-\)\(+\)\(-\)\(16\)
\(+\)\(-\)\(-\)\(+\)\(14\)
\(-\)\(+\)\(+\)\(-\)\(16\)
\(-\)\(+\)\(-\)\(+\)\(14\)
\(-\)\(-\)\(+\)\(+\)\(16\)
\(-\)\(-\)\(-\)\(-\)\(18\)
Plus space\(+\)\(60\)
Minus space\(-\)\(68\)

Trace form

\( 128 q + O(q^{10}) \) \( 128 q + 16 q^{13} + 128 q^{25} + 16 q^{37} + 128 q^{49} - 16 q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8640))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5
8640.2.a.a 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}+2q^{11}-4q^{13}-q^{17}+\cdots\)
8640.2.a.b 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}+6q^{11}+4q^{13}+3q^{17}+\cdots\)
8640.2.a.c 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}-2q^{11}+5q^{13}+8q^{17}+\cdots\)
8640.2.a.d 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+2q^{11}-5q^{13}+2q^{17}+\cdots\)
8640.2.a.e 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{11}-5q^{13}+3q^{17}+\cdots\)
8640.2.a.f 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{11}+q^{13}-3q^{17}+\cdots\)
8640.2.a.g 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-2q^{13}-3q^{17}+5q^{19}+\cdots\)
8640.2.a.h 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+6q^{13}-7q^{17}-7q^{19}+\cdots\)
8640.2.a.i 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+q^{11}-q^{13}-q^{17}+\cdots\)
8640.2.a.j 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+3q^{11}+5q^{13}-3q^{17}+\cdots\)
8640.2.a.k 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+4q^{11}+2q^{13}+5q^{17}+\cdots\)
8640.2.a.l 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-6q^{11}+q^{13}+q^{19}+\cdots\)
8640.2.a.m 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-2q^{11}+3q^{13}-2q^{17}+\cdots\)
8640.2.a.n 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+2q^{11}+5q^{13}-4q^{17}+\cdots\)
8640.2.a.o 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{11}+3q^{17}+q^{19}+3q^{23}+\cdots\)
8640.2.a.p 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{11}+3q^{17}-q^{19}-3q^{23}+\cdots\)
8640.2.a.q 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-2q^{11}+5q^{13}-4q^{17}+\cdots\)
8640.2.a.r 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+2q^{11}+3q^{13}-2q^{17}+\cdots\)
8640.2.a.s 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+6q^{11}+q^{13}-q^{19}+\cdots\)
8640.2.a.t 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-4q^{11}+2q^{13}+5q^{17}+\cdots\)
8640.2.a.u 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{11}+5q^{13}-3q^{17}+\cdots\)
8640.2.a.v 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-q^{11}-q^{13}-q^{17}+\cdots\)
8640.2.a.w 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2q^{13}-3q^{17}-5q^{19}+\cdots\)
8640.2.a.x 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+6q^{13}-7q^{17}+7q^{19}+\cdots\)
8640.2.a.y 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+3q^{11}-5q^{13}+3q^{17}+\cdots\)
8640.2.a.z 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+3q^{11}+q^{13}-3q^{17}+\cdots\)
8640.2.a.ba 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}-2q^{11}-5q^{13}+2q^{17}+\cdots\)
8640.2.a.bb 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}+2q^{11}+5q^{13}+8q^{17}+\cdots\)
8640.2.a.bc 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-6q^{11}+4q^{13}+3q^{17}+\cdots\)
8640.2.a.bd 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-2q^{11}-4q^{13}-q^{17}+\cdots\)
8640.2.a.be 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-6q^{11}+4q^{13}-3q^{17}+\cdots\)
8640.2.a.bf 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-2q^{11}-4q^{13}+q^{17}+\cdots\)
8640.2.a.bg 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{7}-2q^{11}-5q^{13}-2q^{17}+\cdots\)
8640.2.a.bh 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{7}+2q^{11}+5q^{13}-8q^{17}+\cdots\)
8640.2.a.bi 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-4q^{11}+2q^{13}-5q^{17}+\cdots\)
8640.2.a.bj 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-3q^{11}+5q^{13}+3q^{17}+\cdots\)
8640.2.a.bk 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-q^{11}-q^{13}+q^{17}+\cdots\)
8640.2.a.bl 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-2q^{13}+3q^{17}+5q^{19}+\cdots\)
8640.2.a.bm 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+6q^{13}+7q^{17}-7q^{19}+\cdots\)
8640.2.a.bn 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+3q^{11}-5q^{13}-3q^{17}+\cdots\)
8640.2.a.bo 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+3q^{11}+q^{13}+3q^{17}+\cdots\)
8640.2.a.bp 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-2q^{11}+5q^{13}+4q^{17}+\cdots\)
8640.2.a.bq 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+2q^{11}+3q^{13}+2q^{17}+\cdots\)
8640.2.a.br 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+6q^{11}+q^{13}+q^{19}+\cdots\)
8640.2.a.bs 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{11}-3q^{17}-q^{19}+3q^{23}+\cdots\)
8640.2.a.bt 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{11}-3q^{17}+q^{19}-3q^{23}+\cdots\)
8640.2.a.bu 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-6q^{11}+q^{13}-q^{19}+\cdots\)
8640.2.a.bv 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-2q^{11}+3q^{13}+2q^{17}+\cdots\)
8640.2.a.bw 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+2q^{11}+5q^{13}+4q^{17}+\cdots\)
8640.2.a.bx 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{11}-5q^{13}-3q^{17}+\cdots\)
8640.2.a.by 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{11}+q^{13}+3q^{17}+\cdots\)
8640.2.a.bz 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-2q^{13}+3q^{17}-5q^{19}+\cdots\)
8640.2.a.ca 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+6q^{13}+7q^{17}+7q^{19}+\cdots\)
8640.2.a.cb 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+q^{11}-q^{13}+q^{17}+\cdots\)
8640.2.a.cc 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+3q^{11}+5q^{13}+3q^{17}+\cdots\)
8640.2.a.cd 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+4q^{11}+2q^{13}-5q^{17}+\cdots\)
8640.2.a.ce 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}-2q^{11}+5q^{13}-8q^{17}+\cdots\)
8640.2.a.cf 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}+2q^{11}-5q^{13}-2q^{17}+\cdots\)
8640.2.a.cg 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}+2q^{11}-4q^{13}+q^{17}+\cdots\)
8640.2.a.ch 8640.a 1.a $1$ $68.991$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}+6q^{11}+4q^{13}-3q^{17}+\cdots\)
8640.2.a.ci 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(-2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-2+\beta )q^{7}+(2+\beta )q^{11}-\beta q^{13}+\cdots\)
8640.2.a.cj 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta )q^{7}+(2-\beta )q^{11}-q^{13}+\cdots\)
8640.2.a.ck 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta )q^{7}+(1-\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
8640.2.a.cl 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
8640.2.a.cm 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1+\beta )q^{7}+(1+3\beta )q^{11}+\cdots\)
8640.2.a.cn 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{73}) \) None \(0\) \(0\) \(-2\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}+(-1+\beta )q^{11}-3q^{13}+\cdots\)
8640.2.a.co 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}+\beta q^{11}+(2+3\beta )q^{13}+\cdots\)
8640.2.a.cp 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}+\beta q^{11}+(2-3\beta )q^{13}+\cdots\)
8640.2.a.cq 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{73}) \) None \(0\) \(0\) \(-2\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}+(1-\beta )q^{11}-3q^{13}+\cdots\)
8640.2.a.cr 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}+(-1+\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
8640.2.a.cs 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(-2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}+(-1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
8640.2.a.ct 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}+(-1+3\beta )q^{11}+\cdots\)
8640.2.a.cu 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}+(-2+\beta )q^{11}-q^{13}+\cdots\)
8640.2.a.cv 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(-2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(2+\beta )q^{7}+(-2+\beta )q^{11}+\beta q^{13}+\cdots\)
8640.2.a.cw 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(2\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-2+\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
8640.2.a.cx 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta )q^{7}+(-2+\beta )q^{11}+\cdots\)
8640.2.a.cy 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
8640.2.a.cz 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1+\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
8640.2.a.da 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1+\beta )q^{7}+(-1-3\beta )q^{11}+\cdots\)
8640.2.a.db 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{73}) \) None \(0\) \(0\) \(2\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta q^{7}+(1-\beta )q^{11}-3q^{13}+\cdots\)
8640.2.a.dc 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}-\beta q^{11}+(2+3\beta )q^{13}+\cdots\)
8640.2.a.dd 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}-\beta q^{11}+(2-3\beta )q^{13}+\cdots\)
8640.2.a.de 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{73}) \) None \(0\) \(0\) \(2\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+(-1+\beta )q^{11}-3q^{13}+\cdots\)
8640.2.a.df 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+(1-\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
8640.2.a.dg 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+(1+\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
8640.2.a.dh 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+(1-3\beta )q^{11}+(3+\cdots)q^{13}+\cdots\)
8640.2.a.di 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+(2-\beta )q^{11}-q^{13}+\cdots\)
8640.2.a.dj 8640.a 1.a $2$ $68.991$ \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(2+\beta )q^{7}+(2-\beta )q^{11}+\beta q^{13}+\cdots\)
8640.2.a.dk 8640.a 1.a $3$ $68.991$ 3.3.1509.1 None \(0\) \(0\) \(-3\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta _{2}q^{7}+(\beta _{1}+\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)
8640.2.a.dl 8640.a 1.a $3$ $68.991$ 3.3.1509.1 None \(0\) \(0\) \(-3\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta _{2}q^{7}+(-\beta _{1}-\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)
8640.2.a.dm 8640.a 1.a $3$ $68.991$ 3.3.1509.1 None \(0\) \(0\) \(3\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta _{2}q^{7}+(-\beta _{1}-\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)
8640.2.a.dn 8640.a 1.a $3$ $68.991$ 3.3.1509.1 None \(0\) \(0\) \(3\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8640))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8640)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(864))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1080))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2880))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4320))\)\(^{\oplus 2}\)