Properties

Label 9280.2.a
Level $9280$
Weight $2$
Character orbit 9280.a
Rep. character $\chi_{9280}(1,\cdot)$
Character field $\Q$
Dimension $224$
Newform subspaces $73$
Sturm bound $2880$
Trace bound $21$

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Defining parameters

Level: \( N \) \(=\) \( 9280 = 2^{6} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9280.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 73 \)
Sturm bound: \(2880\)
Trace bound: \(21\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9280))\).

Total New Old
Modular forms 1464 224 1240
Cusp forms 1417 224 1193
Eisenstein series 47 0 47

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

\(2\)\(5\)\(29\)FrickeDim
\(+\)\(+\)\(+\)$+$\(26\)
\(+\)\(+\)\(-\)$-$\(30\)
\(+\)\(-\)\(+\)$-$\(30\)
\(+\)\(-\)\(-\)$+$\(26\)
\(-\)\(+\)\(+\)$-$\(30\)
\(-\)\(+\)\(-\)$+$\(26\)
\(-\)\(-\)\(+\)$+$\(26\)
\(-\)\(-\)\(-\)$-$\(30\)
Plus space\(+\)\(104\)
Minus space\(-\)\(120\)

Trace form

\( 224 q + 224 q^{9} + O(q^{10}) \) \( 224 q + 224 q^{9} - 32 q^{13} - 32 q^{21} + 224 q^{25} + 32 q^{33} - 32 q^{37} + 32 q^{41} + 224 q^{49} + 32 q^{57} + 32 q^{69} + 256 q^{81} + 32 q^{85} - 32 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9280))\) 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 5 29
9280.2.a.a 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(-2\) \(-1\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
9280.2.a.b 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(-2\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}-4q^{7}+q^{9}+2q^{13}+\cdots\)
9280.2.a.c 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(-2\) \(1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
9280.2.a.d 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(-2\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
9280.2.a.e 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(-2\) \(1\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+4q^{7}+q^{9}-6q^{13}+\cdots\)
9280.2.a.f 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{9}+4q^{11}+6q^{13}+\cdots\)
9280.2.a.g 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}+2q^{13}-6q^{17}-8q^{19}+\cdots\)
9280.2.a.h 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}+2q^{13}-6q^{17}+8q^{19}+\cdots\)
9280.2.a.i 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{9}-4q^{11}+6q^{13}+\cdots\)
9280.2.a.j 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-3q^{9}-2q^{11}-2q^{13}+\cdots\)
9280.2.a.k 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-3q^{9}-2q^{11}+6q^{13}+\cdots\)
9280.2.a.l 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-3q^{9}+6q^{11}-2q^{13}+\cdots\)
9280.2.a.m 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}-2q^{11}+2q^{13}-2q^{19}+\cdots\)
9280.2.a.n 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}+2q^{11}+2q^{13}+2q^{19}+\cdots\)
9280.2.a.o 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{9}-6q^{11}-2q^{13}+\cdots\)
9280.2.a.p 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{9}+2q^{11}-2q^{13}+\cdots\)
9280.2.a.q 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{9}+2q^{11}+6q^{13}+\cdots\)
9280.2.a.r 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(2\) \(-1\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)
9280.2.a.s 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(2\) \(1\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}-4q^{7}+q^{9}-6q^{13}+\cdots\)
9280.2.a.t 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(2\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
9280.2.a.u 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(2\) \(1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
9280.2.a.v 9280.a 1.a $1$ $74.101$ \(\Q\) None \(0\) \(2\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+4q^{7}+q^{9}+2q^{13}+\cdots\)
9280.2.a.w 9280.a 1.a $2$ $74.101$ \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(-2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
9280.2.a.x 9280.a 1.a $2$ $74.101$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(-2\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+(1+\beta )q^{7}+\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
9280.2.a.y 9280.a 1.a $2$ $74.101$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(2\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+(1-3\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
9280.2.a.z 9280.a 1.a $2$ $74.101$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(2\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+(3-\beta )q^{7}+\beta q^{9}+(2+\cdots)q^{11}+\cdots\)
9280.2.a.ba 9280.a 1.a $2$ $74.101$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}-3q^{9}+\beta q^{11}+2q^{13}+\cdots\)
9280.2.a.bb 9280.a 1.a $2$ $74.101$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(-2\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+(-1-\beta )q^{7}+\beta q^{9}+\cdots\)
9280.2.a.bc 9280.a 1.a $2$ $74.101$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(2\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+(-3+\beta )q^{7}+\beta q^{9}+\cdots\)
9280.2.a.bd 9280.a 1.a $2$ $74.101$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(2\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+(-1+3\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
9280.2.a.be 9280.a 1.a $2$ $74.101$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(-2\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+(-2-\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
9280.2.a.bf 9280.a 1.a $3$ $74.101$ 3.3.621.1 None \(0\) \(-3\) \(3\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
9280.2.a.bg 9280.a 1.a $3$ $74.101$ 3.3.229.1 None \(0\) \(-3\) \(3\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+q^{5}+(2+2\beta _{1}-\beta _{2})q^{7}+\cdots\)
9280.2.a.bh 9280.a 1.a $3$ $74.101$ 3.3.148.1 None \(0\) \(-2\) \(-3\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-q^{5}+(1-\beta _{2})q^{7}+\cdots\)
9280.2.a.bi 9280.a 1.a $3$ $74.101$ 3.3.148.1 None \(0\) \(-2\) \(-3\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-q^{5}+(1+\beta _{1})q^{7}+\cdots\)
9280.2.a.bj 9280.a 1.a $3$ $74.101$ 3.3.148.1 None \(0\) \(-2\) \(-3\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-q^{5}+(1+\beta _{1})q^{7}+\cdots\)
9280.2.a.bk 9280.a 1.a $3$ $74.101$ 3.3.564.1 None \(0\) \(-2\) \(3\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
9280.2.a.bl 9280.a 1.a $3$ $74.101$ 3.3.148.1 None \(0\) \(-2\) \(3\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
9280.2.a.bm 9280.a 1.a $3$ $74.101$ 3.3.148.1 None \(0\) \(-2\) \(3\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(1-\beta _{2})q^{7}+\cdots\)
9280.2.a.bn 9280.a 1.a $3$ $74.101$ 3.3.469.1 None \(0\) \(-1\) \(-3\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(1+\beta _{1}-2\beta _{2})q^{9}+\cdots\)
9280.2.a.bo 9280.a 1.a $3$ $74.101$ 3.3.229.1 None \(0\) \(-1\) \(3\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+q^{5}+(-1+\beta _{1})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
9280.2.a.bp 9280.a 1.a $3$ $74.101$ 3.3.469.1 None \(0\) \(1\) \(-3\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}-q^{5}-\beta _{1}q^{7}+(1+\beta _{1}-2\beta _{2})q^{9}+\cdots\)
9280.2.a.bq 9280.a 1.a $3$ $74.101$ 3.3.229.1 None \(0\) \(1\) \(3\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+q^{5}+(1-\beta _{1})q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots\)
9280.2.a.br 9280.a 1.a $3$ $74.101$ 3.3.148.1 None \(0\) \(2\) \(-3\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
9280.2.a.bs 9280.a 1.a $3$ $74.101$ 3.3.148.1 None \(0\) \(2\) \(-3\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
9280.2.a.bt 9280.a 1.a $3$ $74.101$ 3.3.148.1 None \(0\) \(2\) \(-3\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
9280.2.a.bu 9280.a 1.a $3$ $74.101$ 3.3.148.1 None \(0\) \(2\) \(3\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
9280.2.a.bv 9280.a 1.a $3$ $74.101$ 3.3.148.1 None \(0\) \(2\) \(3\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+(1-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
9280.2.a.bw 9280.a 1.a $3$ $74.101$ 3.3.564.1 None \(0\) \(2\) \(3\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+q^{5}+(1-\beta _{2})q^{7}+(4+\cdots)q^{9}+\cdots\)
9280.2.a.bx 9280.a 1.a $3$ $74.101$ 3.3.229.1 None \(0\) \(3\) \(3\) \(-7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+q^{5}+(-2-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
9280.2.a.by 9280.a 1.a $3$ $74.101$ 3.3.621.1 None \(0\) \(3\) \(3\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
9280.2.a.bz 9280.a 1.a $4$ $74.101$ 4.4.11344.1 None \(0\) \(-2\) \(4\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+q^{5}+\beta _{3}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
9280.2.a.ca 9280.a 1.a $4$ $74.101$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-q^{5}-\beta _{3}q^{7}-q^{9}-\beta _{2}q^{11}+\cdots\)
9280.2.a.cb 9280.a 1.a $4$ $74.101$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-q^{5}+\beta _{2}q^{7}-q^{9}+\beta _{2}q^{11}+\cdots\)
9280.2.a.cc 9280.a 1.a $4$ $74.101$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+q^{5}-\beta _{2}q^{7}-q^{9}+\beta _{3}q^{11}+\cdots\)
9280.2.a.cd 9280.a 1.a $4$ $74.101$ \(\Q(\sqrt{6}, \sqrt{26})\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+\beta _{1}q^{7}+3q^{9}-\beta _{2}q^{11}+\cdots\)
9280.2.a.ce 9280.a 1.a $4$ $74.101$ \(\Q(\sqrt{6}, \sqrt{10})\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+q^{5}+\beta _{3}q^{7}+3q^{9}+\beta _{3}q^{11}+\cdots\)
9280.2.a.cf 9280.a 1.a $4$ $74.101$ 4.4.11344.1 None \(0\) \(2\) \(4\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+q^{5}-\beta _{3}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
9280.2.a.cg 9280.a 1.a $5$ $74.101$ 5.5.580484.1 None \(0\) \(-3\) \(-5\) \(7\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{3}-q^{5}+(1-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
9280.2.a.ch 9280.a 1.a $5$ $74.101$ 5.5.6083172.1 None \(0\) \(-1\) \(-5\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(\beta _{2}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
9280.2.a.ci 9280.a 1.a $5$ $74.101$ 5.5.3145252.1 None \(0\) \(-1\) \(5\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+q^{5}+(-1+\beta _{2})q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
9280.2.a.cj 9280.a 1.a $5$ $74.101$ 5.5.6083172.1 None \(0\) \(1\) \(-5\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-\beta _{2}+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
9280.2.a.ck 9280.a 1.a $5$ $74.101$ 5.5.3145252.1 None \(0\) \(1\) \(5\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+q^{5}+(1-\beta _{2})q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
9280.2.a.cl 9280.a 1.a $5$ $74.101$ 5.5.580484.1 None \(0\) \(3\) \(-5\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{3}-q^{5}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
9280.2.a.cm 9280.a 1.a $6$ $74.101$ 6.6.39643024.1 None \(0\) \(-1\) \(-6\) \(5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
9280.2.a.cn 9280.a 1.a $6$ $74.101$ 6.6.26118032.1 None \(0\) \(-1\) \(6\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
9280.2.a.co 9280.a 1.a $6$ $74.101$ 6.6.39643024.1 None \(0\) \(1\) \(-6\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
9280.2.a.cp 9280.a 1.a $6$ $74.101$ 6.6.26118032.1 None \(0\) \(1\) \(6\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
9280.2.a.cq 9280.a 1.a $7$ $74.101$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-1\) \(-7\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(-\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)
9280.2.a.cr 9280.a 1.a $7$ $74.101$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(1\) \(-7\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(\beta _{1}-\beta _{5})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9280.2.a.cs 9280.a 1.a $8$ $74.101$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-8\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-\beta _{1}-\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)
9280.2.a.ct 9280.a 1.a $10$ $74.101$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-10\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+\beta _{7}q^{7}+(3+\beta _{2})q^{9}+\cdots\)
9280.2.a.cu 9280.a 1.a $10$ $74.101$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(10\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}-\beta _{9}q^{7}+(2+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(290))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(464))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(580))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(928))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1856))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4640))\)\(^{\oplus 2}\)