Properties

Label 5376.2.c
Level $5376$
Weight $2$
Character orbit 5376.c
Rep. character $\chi_{5376}(2689,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $40$
Sturm bound $2048$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 5376 = 2^{8} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5376.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 40 \)
Sturm bound: \(2048\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(23\), \(31\), \(47\), \(71\), \(79\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5376, [\chi])\).

Total New Old
Modular forms 1072 96 976
Cusp forms 976 96 880
Eisenstein series 96 0 96

Trace form

\( 96 q - 96 q^{9} + O(q^{10}) \) \( 96 q - 96 q^{9} - 96 q^{25} + 96 q^{49} + 64 q^{65} - 64 q^{73} + 96 q^{81} - 64 q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5376, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5376.2.c.a 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 2688.2.a.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{5}-q^{7}-q^{9}-6iq^{11}+\cdots\)
5376.2.c.b 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 672.2.a.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{5}-q^{7}-q^{9}+2iq^{11}+\cdots\)
5376.2.c.c 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 2688.2.a.b \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{5}-q^{7}-q^{9}+4iq^{11}+\cdots\)
5376.2.c.d 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 168.2.a.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-6iq^{13}+\cdots\)
5376.2.c.e 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 42.2.a.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-4iq^{11}+\cdots\)
5376.2.c.f 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 168.2.a.b \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{5}-q^{7}-q^{9}+2iq^{13}+\cdots\)
5376.2.c.g 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 2688.2.a.e \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-q^{7}-q^{9}-2iq^{11}-6q^{17}+\cdots\)
5376.2.c.h 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 2688.2.a.d \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-q^{7}-q^{9}-2iq^{11}+4iq^{13}+\cdots\)
5376.2.c.i 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 84.2.a.b \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{7}-q^{9}+6iq^{11}+2iq^{13}+\cdots\)
5376.2.c.j 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 672.2.a.c \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{7}-q^{9}-2iq^{11}-2iq^{13}+\cdots\)
5376.2.c.k 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 2688.2.a.f \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{7}-q^{9}+6iq^{11}-4iq^{13}+\cdots\)
5376.2.c.l 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 21.2.a.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2iq^{5}-q^{7}-q^{9}+4iq^{11}+\cdots\)
5376.2.c.m 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 672.2.a.b \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2iq^{5}-q^{7}-q^{9}-4iq^{11}+\cdots\)
5376.2.c.n 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 2688.2.a.c \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2iq^{5}-q^{7}-q^{9}+2q^{15}+\cdots\)
5376.2.c.o 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 672.2.a.d \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{13}+\cdots\)
5376.2.c.p 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 84.2.a.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+4iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
5376.2.c.q 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 84.2.a.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)
5376.2.c.r 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 21.2.a.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}-4iq^{11}+\cdots\)
5376.2.c.s 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 672.2.a.b \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}+4iq^{11}+\cdots\)
5376.2.c.t 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 2688.2.a.c \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}-2q^{15}+\cdots\)
5376.2.c.u 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 672.2.a.d \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}-2iq^{13}+\cdots\)
5376.2.c.v 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 2688.2.a.e \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+q^{7}-q^{9}-2iq^{11}-6q^{17}+\cdots\)
5376.2.c.w 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 2688.2.a.d \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+q^{7}-q^{9}-2iq^{11}-4iq^{13}+\cdots\)
5376.2.c.x 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 84.2.a.b \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+q^{7}-q^{9}+6iq^{11}-2iq^{13}+\cdots\)
5376.2.c.y 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 672.2.a.c \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+q^{7}-q^{9}-2iq^{11}+2iq^{13}+\cdots\)
5376.2.c.z 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 2688.2.a.f \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+q^{7}-q^{9}-6iq^{11}-4iq^{13}+\cdots\)
5376.2.c.ba 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 2688.2.a.b \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2iq^{5}+q^{7}-q^{9}-4iq^{11}+\cdots\)
5376.2.c.bb 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 168.2.a.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2iq^{5}+q^{7}-q^{9}-6iq^{13}+\cdots\)
5376.2.c.bc 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 42.2.a.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2iq^{5}+q^{7}-q^{9}+4iq^{11}+\cdots\)
5376.2.c.bd 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 168.2.a.b \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{13}+\cdots\)
5376.2.c.be 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 2688.2.a.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+4iq^{5}+q^{7}-q^{9}+6iq^{11}+\cdots\)
5376.2.c.bf 5376.c 8.b $2$ $42.928$ \(\Q(\sqrt{-1}) \) None 672.2.a.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+4iq^{5}+q^{7}-q^{9}-2iq^{11}+\cdots\)
5376.2.c.bg 5376.c 8.b $4$ $42.928$ \(\Q(\zeta_{8})\) None 2688.2.a.ba \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}-q^{7}-q^{9}+(2\zeta_{8}+\cdots)q^{11}+\cdots\)
5376.2.c.bh 5376.c 8.b $4$ $42.928$ \(\Q(\zeta_{12})\) None 672.2.a.i \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-q^{7}-q^{9}+(-2\zeta_{12}+\cdots)q^{11}+\cdots\)
5376.2.c.bi 5376.c 8.b $4$ $42.928$ \(\Q(i, \sqrt{5})\) None 2688.2.a.y \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}-q^{9}+\cdots\)
5376.2.c.bj 5376.c 8.b $4$ $42.928$ \(\Q(i, \sqrt{5})\) None 2688.2.a.z \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}-q^{9}+\cdots\)
5376.2.c.bk 5376.c 8.b $4$ $42.928$ \(\Q(i, \sqrt{5})\) None 2688.2.a.y \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-q^{9}+\cdots\)
5376.2.c.bl 5376.c 8.b $4$ $42.928$ \(\Q(i, \sqrt{5})\) None 2688.2.a.z \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-q^{9}+\cdots\)
5376.2.c.bm 5376.c 8.b $4$ $42.928$ \(\Q(\zeta_{8})\) None 2688.2.a.ba \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+q^{7}-q^{9}+(-2\zeta_{8}+\cdots)q^{11}+\cdots\)
5376.2.c.bn 5376.c 8.b $4$ $42.928$ \(\Q(\zeta_{12})\) None 672.2.a.i \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+q^{7}-q^{9}+(-2\zeta_{12}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5376, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5376, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1792, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2688, [\chi])\)\(^{\oplus 2}\)