Properties

Label 5760.2.k
Level $5760$
Weight $2$
Character orbit 5760.k
Rep. character $\chi_{5760}(2881,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $25$
Sturm bound $2304$
Trace bound $41$

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Defining parameters

Level: \( N \) \(=\) \( 5760 = 2^{7} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5760.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 25 \)
Sturm bound: \(2304\)
Trace bound: \(41\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5760, [\chi])\).

Total New Old
Modular forms 1216 80 1136
Cusp forms 1088 80 1008
Eisenstein series 128 0 128

Trace form

\( 80 q + O(q^{10}) \) \( 80 q - 80 q^{25} + 32 q^{41} + 16 q^{49} + 64 q^{73} - 32 q^{89} - 64 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5760, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5760.2.k.a 5760.k 8.b $2$ $45.994$ \(\Q(\sqrt{-1}) \) None 5760.2.k.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{5}-4 q^{7}-4 q^{17}-4 i q^{19}+\cdots\)
5760.2.k.b 5760.k 8.b $2$ $45.994$ \(\Q(\sqrt{-1}) \) None 5760.2.k.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{5}-4 q^{7}+4 q^{17}+4 i q^{19}+\cdots\)
5760.2.k.c 5760.k 8.b $2$ $45.994$ \(\Q(\sqrt{-1}) \) None 1920.2.k.d \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{5}-2 q^{7}-6 i q^{11}-6 i q^{13}+\cdots\)
5760.2.k.d 5760.k 8.b $2$ $45.994$ \(\Q(\sqrt{-1}) \) None 1920.2.k.c \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{5}-2 q^{7}+2 i q^{11}+2 i q^{13}+\cdots\)
5760.2.k.e 5760.k 8.b $2$ $45.994$ \(\Q(\sqrt{-1}) \) None 1920.2.k.b \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{5}-2 q^{7}-2 i q^{11}-2 i q^{13}+\cdots\)
5760.2.k.f 5760.k 8.b $2$ $45.994$ \(\Q(\sqrt{-1}) \) None 1920.2.k.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{5}-2 q^{7}+2 i q^{11}+2 i q^{13}+\cdots\)
5760.2.k.g 5760.k 8.b $2$ $45.994$ \(\Q(\sqrt{-1}) \) None 1920.2.k.c \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{5}+2 q^{7}-2 i q^{11}+2 i q^{13}+\cdots\)
5760.2.k.h 5760.k 8.b $2$ $45.994$ \(\Q(\sqrt{-1}) \) None 1920.2.k.d \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{5}+2 q^{7}+6 i q^{11}-6 i q^{13}+\cdots\)
5760.2.k.i 5760.k 8.b $2$ $45.994$ \(\Q(\sqrt{-1}) \) None 1920.2.k.b \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{5}+2 q^{7}-2 i q^{11}+2 i q^{13}+\cdots\)
5760.2.k.j 5760.k 8.b $2$ $45.994$ \(\Q(\sqrt{-1}) \) None 1920.2.k.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{5}+2 q^{7}+2 i q^{11}-2 i q^{13}+\cdots\)
5760.2.k.k 5760.k 8.b $2$ $45.994$ \(\Q(\sqrt{-1}) \) None 5760.2.k.a \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{5}+4 q^{7}-4 q^{17}-4 i q^{19}+\cdots\)
5760.2.k.l 5760.k 8.b $2$ $45.994$ \(\Q(\sqrt{-1}) \) None 5760.2.k.a \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{5}+4 q^{7}+4 q^{17}-4 i q^{19}+\cdots\)
5760.2.k.m 5760.k 8.b $4$ $45.994$ \(\Q(\zeta_{8})\) None 1920.2.k.j \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_1 q^{5}-2 q^{7}+(-\beta_{2}-2\beta_1)q^{11}+\cdots\)
5760.2.k.n 5760.k 8.b $4$ $45.994$ \(\Q(\zeta_{8})\) None 1920.2.k.i \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_1 q^{5}+(\beta_{3}-2)q^{7}+(-\beta_{2}-2\beta_1)q^{11}+\cdots\)
5760.2.k.o 5760.k 8.b $4$ $45.994$ \(\Q(\zeta_{8})\) None 640.2.d.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{5}-3\beta_{3} q^{7}+4\beta_{2} q^{11}-2\beta_1 q^{13}+\cdots\)
5760.2.k.p 5760.k 8.b $4$ $45.994$ \(\Q(\zeta_{8})\) None 5760.2.k.p \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_1 q^{5}+\beta_{3} q^{7}+\beta_{2} q^{11}-4\beta_1 q^{13}+\cdots\)
5760.2.k.q 5760.k 8.b $4$ $45.994$ \(\Q(\zeta_{8})\) None 640.2.d.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{5}-\beta_{3} q^{7}-2\beta_{2} q^{11}+2\beta_1 q^{13}+\cdots\)
5760.2.k.r 5760.k 8.b $4$ $45.994$ \(\Q(\zeta_{8})\) None 5760.2.k.r \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{5}-\beta_{2} q^{11}-4\beta_1 q^{13}+\beta_{2} q^{19}+\cdots\)
5760.2.k.s 5760.k 8.b $4$ $45.994$ \(\Q(\zeta_{8})\) None 5760.2.k.r \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{5}-\beta_{2} q^{11}+4\beta_1 q^{13}-\beta_{2} q^{19}+\cdots\)
5760.2.k.t 5760.k 8.b $4$ $45.994$ \(\Q(i, \sqrt{10})\) None 640.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}-\beta _{3}q^{7}+6\beta _{1}q^{13}+2q^{17}+\cdots\)
5760.2.k.u 5760.k 8.b $4$ $45.994$ \(\Q(\zeta_{8})\) None 5760.2.k.p \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_1 q^{5}+\beta_{3} q^{7}+\beta_{2} q^{11}+4\beta_1 q^{13}+\cdots\)
5760.2.k.v 5760.k 8.b $4$ $45.994$ \(\Q(\zeta_{8})\) None 640.2.d.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_1 q^{5}+3\beta_{3} q^{7}-2\beta_{2} q^{11}+6\beta_1 q^{13}+\cdots\)
5760.2.k.w 5760.k 8.b $4$ $45.994$ \(\Q(\zeta_{8})\) None 1920.2.k.i \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{5}+(\beta_{3}+2)q^{7}+(\beta_{2}-2\beta_1)q^{11}+\cdots\)
5760.2.k.x 5760.k 8.b $4$ $45.994$ \(\Q(\zeta_{8})\) None 1920.2.k.j \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{5}+2 q^{7}+(\beta_{2}-2\beta_1)q^{11}+\cdots\)
5760.2.k.y 5760.k 8.b $8$ $45.994$ \(\Q(\zeta_{24})\) None 5760.2.k.y \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_1 q^{5}-\beta_{2} q^{11}+\beta_{5} q^{13}-\beta_{3} q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5760, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1920, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2880, [\chi])\)\(^{\oplus 2}\)