Properties

Label 2320.2.a
Level $2320$
Weight $2$
Character orbit 2320.a
Rep. character $\chi_{2320}(1,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $23$
Sturm bound $720$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2320 = 2^{4} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2320.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(720\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2320))\).

Total New Old
Modular forms 372 56 316
Cusp forms 349 56 293
Eisenstein series 23 0 23

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
\(+\)\(+\)\(+\)$+$\(6\)
\(+\)\(+\)\(-\)$-$\(8\)
\(+\)\(-\)\(+\)$-$\(8\)
\(+\)\(-\)\(-\)$+$\(6\)
\(-\)\(+\)\(+\)$-$\(8\)
\(-\)\(+\)\(-\)$+$\(6\)
\(-\)\(-\)\(+\)$+$\(6\)
\(-\)\(-\)\(-\)$-$\(8\)
Plus space\(+\)\(24\)
Minus space\(-\)\(32\)

Trace form

\( 56 q - 4 q^{3} - 8 q^{7} + 64 q^{9} + O(q^{10}) \) \( 56 q - 4 q^{3} - 8 q^{7} + 64 q^{9} + 4 q^{15} + 8 q^{17} + 56 q^{25} - 16 q^{27} - 24 q^{31} - 8 q^{39} - 44 q^{43} - 4 q^{47} + 48 q^{49} + 48 q^{51} + 8 q^{55} - 16 q^{57} - 8 q^{59} - 16 q^{61} + 8 q^{63} + 8 q^{65} - 8 q^{67} + 16 q^{69} + 16 q^{71} + 8 q^{73} - 4 q^{75} + 32 q^{77} - 24 q^{79} + 72 q^{81} + 40 q^{83} - 16 q^{85} + 12 q^{87} + 16 q^{89} + 32 q^{93} + 16 q^{95} + 8 q^{97} + 32 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2320))\) 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
2320.2.a.a 2320.a 1.a $1$ $18.525$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-4q^{7}+q^{9}+6q^{13}+\cdots\)
2320.2.a.b 2320.a 1.a $1$ $18.525$ \(\Q\) None \(0\) \(-2\) \(-1\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+4q^{7}+q^{9}-2q^{13}+\cdots\)
2320.2.a.c 2320.a 1.a $1$ $18.525$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}+2q^{11}-2q^{13}+2q^{19}+\cdots\)
2320.2.a.d 2320.a 1.a $1$ $18.525$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{9}-2q^{11}-6q^{13}+\cdots\)
2320.2.a.e 2320.a 1.a $1$ $18.525$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{9}+6q^{11}+2q^{13}+\cdots\)
2320.2.a.f 2320.a 1.a $1$ $18.525$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}-2q^{13}-6q^{17}+8q^{19}+\cdots\)
2320.2.a.g 2320.a 1.a $1$ $18.525$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{9}+4q^{11}-6q^{13}+\cdots\)
2320.2.a.h 2320.a 1.a $1$ $18.525$ \(\Q\) None \(0\) \(2\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
2320.2.a.i 2320.a 1.a $2$ $18.525$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(-2\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+(-3+\beta )q^{7}+\beta q^{9}+\cdots\)
2320.2.a.j 2320.a 1.a $2$ $18.525$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(2\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+(-1-\beta )q^{7}+\beta q^{9}+\cdots\)
2320.2.a.k 2320.a 1.a $2$ $18.525$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+(2-\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
2320.2.a.l 2320.a 1.a $3$ $18.525$ 3.3.621.1 None \(0\) \(-3\) \(-3\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2320.2.a.m 2320.a 1.a $3$ $18.525$ 3.3.564.1 None \(0\) \(-2\) \(-3\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-q^{5}+(1-\beta _{2})q^{7}+\cdots\)
2320.2.a.n 2320.a 1.a $3$ $18.525$ 3.3.148.1 None \(0\) \(-2\) \(3\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
2320.2.a.o 2320.a 1.a $3$ $18.525$ 3.3.148.1 None \(0\) \(-2\) \(3\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
2320.2.a.p 2320.a 1.a $3$ $18.525$ 3.3.229.1 None \(0\) \(-1\) \(-3\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-q^{5}+(1-\beta _{1})q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots\)
2320.2.a.q 2320.a 1.a $3$ $18.525$ 3.3.469.1 None \(0\) \(1\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+q^{5}+\beta _{1}q^{7}+(1+\beta _{1}-2\beta _{2})q^{9}+\cdots\)
2320.2.a.r 2320.a 1.a $3$ $18.525$ 3.3.148.1 None \(0\) \(2\) \(-3\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
2320.2.a.s 2320.a 1.a $3$ $18.525$ 3.3.148.1 None \(0\) \(2\) \(-3\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-q^{5}+(1-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
2320.2.a.t 2320.a 1.a $3$ $18.525$ 3.3.148.1 None \(0\) \(2\) \(3\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+(1+\beta _{1})q^{7}+(1+\cdots)q^{9}+\cdots\)
2320.2.a.u 2320.a 1.a $5$ $18.525$ 5.5.580484.1 None \(0\) \(-3\) \(5\) \(-7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{3}+q^{5}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
2320.2.a.v 2320.a 1.a $5$ $18.525$ 5.5.3145252.1 None \(0\) \(1\) \(-5\) \(-7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}-q^{5}+(-1+\beta _{2})q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
2320.2.a.w 2320.a 1.a $5$ $18.525$ 5.5.6083172.1 None \(0\) \(1\) \(5\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(\beta _{2}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2320))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2320)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(290))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(464))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(580))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1160))\)\(^{\oplus 2}\)