Properties

Label 2304.2.d
Level $2304$
Weight $2$
Character orbit 2304.d
Rep. character $\chi_{2304}(1153,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $19$
Sturm bound $768$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2304.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(768\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2304, [\chi])\).

Total New Old
Modular forms 432 42 390
Cusp forms 336 38 298
Eisenstein series 96 4 92

Trace form

\( 38 q + O(q^{10}) \) \( 38 q + 4 q^{17} - 26 q^{25} - 4 q^{41} - 10 q^{49} + 40 q^{65} + 20 q^{73} - 20 q^{89} - 36 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2304.2.d.a 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) 36.2.a.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{7}-iq^{13}+4iq^{19}+5q^{25}+\cdots\)
2304.2.d.b 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 128.2.a.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}-4q^{7}+iq^{11}+iq^{13}+2q^{17}+\cdots\)
2304.2.d.c 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 96.2.a.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}-4q^{7}-2iq^{11}-iq^{13}+6q^{17}+\cdots\)
2304.2.d.d 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 384.2.a.b \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{7}+2iq^{11}-3iq^{13}-6q^{17}+\cdots\)
2304.2.d.e 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 1152.2.a.d \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}-2q^{7}+2iq^{11}+iq^{13}-4q^{17}+\cdots\)
2304.2.d.f 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 384.2.a.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{5}-2q^{7}-2iq^{11}-iq^{13}+\cdots\)
2304.2.d.g 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 1152.2.a.d \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}-2q^{7}+2iq^{11}-iq^{13}+4q^{17}+\cdots\)
2304.2.d.h 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 288.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2iq^{5}-3iq^{13}-8q^{17}-11q^{25}+\cdots\)
2304.2.d.i 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 24.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}-2iq^{11}+iq^{13}-2q^{17}+\cdots\)
2304.2.d.j 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 32.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}-3iq^{13}-2q^{17}+q^{25}-5iq^{29}+\cdots\)
2304.2.d.k 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 24.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+2iq^{11}+iq^{13}-2q^{17}+\cdots\)
2304.2.d.l 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 288.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2iq^{5}+3iq^{13}+8q^{17}-11q^{25}+\cdots\)
2304.2.d.m 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 384.2.a.b \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{7}-2iq^{11}-3iq^{13}-6q^{17}+\cdots\)
2304.2.d.n 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 1152.2.a.d \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+2q^{7}-2iq^{11}+iq^{13}-4q^{17}+\cdots\)
2304.2.d.o 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 384.2.a.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{5}+2q^{7}+2iq^{11}-iq^{13}+\cdots\)
2304.2.d.p 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 1152.2.a.d \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+2q^{7}-2iq^{11}-iq^{13}+4q^{17}+\cdots\)
2304.2.d.q 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) 36.2.a.a \(0\) \(0\) \(0\) \(8\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{7}-iq^{13}-4iq^{19}+5q^{25}+\cdots\)
2304.2.d.r 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 128.2.a.a \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+4q^{7}-iq^{11}+iq^{13}+2q^{17}+\cdots\)
2304.2.d.s 2304.d 8.b $2$ $18.398$ \(\Q(\sqrt{-1}) \) None 96.2.a.a \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+4q^{7}+2iq^{11}-iq^{13}+6q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2304, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)