Properties

Label 7920.2.a
Level $7920$
Weight $2$
Character orbit 7920.a
Rep. character $\chi_{7920}(1,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $66$
Sturm bound $3456$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7920.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 66 \)
Sturm bound: \(3456\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(13\), \(17\), \(19\), \(23\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7920))\).

Total New Old
Modular forms 1776 100 1676
Cusp forms 1681 100 1581
Eisenstein series 95 0 95

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

\(2\)\(3\)\(5\)\(11\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(5\)
\(+\)\(+\)\(+\)\(-\)$-$\(5\)
\(+\)\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(+\)\(-\)\(-\)$+$\(5\)
\(+\)\(-\)\(+\)\(+\)$-$\(7\)
\(+\)\(-\)\(+\)\(-\)$+$\(7\)
\(+\)\(-\)\(-\)\(+\)$+$\(8\)
\(+\)\(-\)\(-\)\(-\)$-$\(8\)
\(-\)\(+\)\(+\)\(+\)$-$\(7\)
\(-\)\(+\)\(+\)\(-\)$+$\(3\)
\(-\)\(+\)\(-\)\(+\)$+$\(3\)
\(-\)\(+\)\(-\)\(-\)$-$\(7\)
\(-\)\(-\)\(+\)\(+\)$+$\(7\)
\(-\)\(-\)\(+\)\(-\)$-$\(9\)
\(-\)\(-\)\(-\)\(+\)$-$\(8\)
\(-\)\(-\)\(-\)\(-\)$+$\(6\)
Plus space\(+\)\(44\)
Minus space\(-\)\(56\)

Trace form

\( 100 q + 8 q^{7} + O(q^{10}) \) \( 100 q + 8 q^{7} - 12 q^{23} + 100 q^{25} - 8 q^{29} - 24 q^{31} - 16 q^{43} - 20 q^{47} + 116 q^{49} + 4 q^{55} - 16 q^{59} + 16 q^{61} - 4 q^{67} - 16 q^{71} + 16 q^{73} - 64 q^{83} + 16 q^{85} + 16 q^{89} + 24 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7920))\) 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 11
7920.2.a.a 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}-q^{11}-4q^{13}+2q^{17}+\cdots\)
7920.2.a.b 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}-q^{11}+6q^{13}+6q^{17}+\cdots\)
7920.2.a.c 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}+q^{11}+2q^{13}+2q^{17}+\cdots\)
7920.2.a.d 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+q^{11}-6q^{13}+7q^{17}+\cdots\)
7920.2.a.e 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-q^{11}-6q^{13}-3q^{17}+\cdots\)
7920.2.a.f 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{11}-2q^{13}-2q^{17}-4q^{19}+\cdots\)
7920.2.a.g 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)
7920.2.a.h 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{11}-2q^{13}+6q^{17}+4q^{19}+\cdots\)
7920.2.a.i 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{11}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
7920.2.a.j 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{11}-6q^{13}+6q^{17}+q^{25}+\cdots\)
7920.2.a.k 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{11}-2q^{17}-2q^{19}+6q^{23}+\cdots\)
7920.2.a.l 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{11}+4q^{17}+4q^{19}+6q^{23}+\cdots\)
7920.2.a.m 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{11}+6q^{13}-2q^{17}+4q^{19}+\cdots\)
7920.2.a.n 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-q^{11}-4q^{13}-6q^{17}+\cdots\)
7920.2.a.o 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-q^{11}-4q^{13}+4q^{19}+\cdots\)
7920.2.a.p 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-q^{11}+2q^{13}-6q^{17}+\cdots\)
7920.2.a.q 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}+q^{11}-6q^{13}+2q^{17}+\cdots\)
7920.2.a.r 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots\)
7920.2.a.s 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(-5\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-5q^{7}+q^{11}+2q^{13}-3q^{17}+\cdots\)
7920.2.a.t 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-q^{11}+2q^{13}-2q^{17}+\cdots\)
7920.2.a.u 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-q^{11}+2q^{13}-2q^{17}+\cdots\)
7920.2.a.v 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}+q^{11}-4q^{13}-2q^{17}+\cdots\)
7920.2.a.w 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-q^{11}-4q^{13}+4q^{19}+\cdots\)
7920.2.a.x 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+q^{11}-4q^{17}+4q^{19}+\cdots\)
7920.2.a.y 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+q^{11}+2q^{13}-2q^{19}+\cdots\)
7920.2.a.z 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{11}+2q^{17}-2q^{19}-6q^{23}+\cdots\)
7920.2.a.ba 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{11}-4q^{13}+2q^{17}-2q^{19}+\cdots\)
7920.2.a.bb 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{11}+2q^{13}+2q^{17}-8q^{19}+\cdots\)
7920.2.a.bc 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-q^{11}+2q^{13}+3q^{17}+\cdots\)
7920.2.a.bd 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-q^{11}-4q^{13}-4q^{17}+\cdots\)
7920.2.a.be 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-q^{11}-4q^{13}+4q^{17}+\cdots\)
7920.2.a.bf 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-q^{11}-4q^{17}-4q^{19}+\cdots\)
7920.2.a.bg 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-q^{11}+8q^{19}-8q^{23}+\cdots\)
7920.2.a.bh 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-q^{11}+2q^{13}-8q^{17}+\cdots\)
7920.2.a.bi 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+q^{11}-4q^{13}+4q^{17}+\cdots\)
7920.2.a.bj 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+q^{11}+8q^{17}+8q^{19}+\cdots\)
7920.2.a.bk 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+q^{11}+4q^{13}+4q^{19}+\cdots\)
7920.2.a.bl 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}-q^{11}-4q^{13}+6q^{17}+\cdots\)
7920.2.a.bm 7920.a 1.a $1$ $63.242$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}+q^{11}-4q^{13}+6q^{17}+\cdots\)
7920.2.a.bn 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta )q^{7}-q^{11}+(3-\beta )q^{13}+\cdots\)
7920.2.a.bo 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta )q^{7}+q^{11}+(-1-\beta )q^{13}+\cdots\)
7920.2.a.bp 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1+\beta )q^{7}+q^{11}+(1-\beta )q^{13}+\cdots\)
7920.2.a.bq 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-2\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}-q^{11}+2q^{13}+(2-\beta )q^{17}+\cdots\)
7920.2.a.br 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}-q^{11}+(-2-\beta )q^{13}+\cdots\)
7920.2.a.bs 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}-q^{11}+(2+\beta )q^{13}+(-2+\cdots)q^{17}+\cdots\)
7920.2.a.bt 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}+q^{11}+(2+\beta )q^{13}+(-2+\cdots)q^{17}+\cdots\)
7920.2.a.bu 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}+q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
7920.2.a.bv 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}-q^{11}+(-1+3\beta )q^{13}+\cdots\)
7920.2.a.bw 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(2+\beta )q^{7}-q^{11}-\beta q^{13}+3\beta q^{17}+\cdots\)
7920.2.a.bx 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(2+\beta )q^{7}+q^{11}-\beta q^{13}-3\beta q^{17}+\cdots\)
7920.2.a.by 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-5\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(-2-\beta )q^{7}-q^{11}+(4-2\beta )q^{13}+\cdots\)
7920.2.a.bz 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-q^{11}+(2+\beta )q^{13}+(-2+\cdots)q^{19}+\cdots\)
7920.2.a.ca 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta )q^{7}+q^{11}+(2-2\beta )q^{13}+\cdots\)
7920.2.a.cb 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1+\beta )q^{7}-q^{11}+(1-\beta )q^{13}+\cdots\)
7920.2.a.cc 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+q^{11}+(-2-\beta )q^{13}+\cdots\)
7920.2.a.cd 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+q^{11}+(-1+3\beta )q^{13}+\cdots\)
7920.2.a.ce 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+q^{11}+(1-\beta )q^{13}+\cdots\)
7920.2.a.cf 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(2+\beta )q^{7}-q^{11}-\beta q^{13}+3\beta q^{17}+\cdots\)
7920.2.a.cg 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(2+\beta )q^{7}-q^{11}+2\beta q^{13}+\cdots\)
7920.2.a.ch 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+q^{11}+(-4+\beta )q^{13}+\cdots\)
7920.2.a.ci 7920.a 1.a $2$ $63.242$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(2+\beta )q^{7}+q^{11}-\beta q^{13}-3\beta q^{17}+\cdots\)
7920.2.a.cj 7920.a 1.a $3$ $63.242$ 3.3.148.1 None \(0\) \(0\) \(-3\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta _{2}q^{7}+q^{11}+(-1-\beta _{1})q^{13}+\cdots\)
7920.2.a.ck 7920.a 1.a $3$ $63.242$ 3.3.1016.1 None \(0\) \(0\) \(-3\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta _{2}q^{7}+q^{11}+(1-\beta _{1}-\beta _{2})q^{13}+\cdots\)
7920.2.a.cl 7920.a 1.a $3$ $63.242$ 3.3.1016.1 None \(0\) \(0\) \(3\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta _{2}q^{7}-q^{11}+(1-\beta _{1}-\beta _{2})q^{13}+\cdots\)
7920.2.a.cm 7920.a 1.a $4$ $63.242$ 4.4.48704.2 None \(0\) \(0\) \(-4\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta _{3})q^{7}-q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots\)
7920.2.a.cn 7920.a 1.a $4$ $63.242$ 4.4.48704.2 None \(0\) \(0\) \(4\) \(-4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta _{3})q^{7}+q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7920)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(660))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(792))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(880))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(990))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1584))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1980))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2640))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3960))\)\(^{\oplus 2}\)