Properties

Label 2304.2.c
Level $2304$
Weight $2$
Character orbit 2304.c
Rep. character $\chi_{2304}(2303,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $10$
Sturm bound $768$
Trace bound $49$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2304.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(768\)
Trace bound: \(49\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 432 32 400
Cusp forms 336 32 304
Eisenstein series 96 0 96

Trace form

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2304.2.c.a \(2\) \(18.398\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-2\beta q^{7}-4q^{11}-2q^{13}+\beta q^{17}+\cdots\)
2304.2.c.b \(2\) \(18.398\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-2\beta q^{7}-4q^{11}+2q^{13}-\beta q^{17}+\cdots\)
2304.2.c.c \(2\) \(18.398\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+3\beta q^{5}-6q^{13}-5\beta q^{17}-13q^{25}+\cdots\)
2304.2.c.d \(2\) \(18.398\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-6q^{13}-3\beta q^{17}+3q^{25}+\cdots\)
2304.2.c.e \(2\) \(18.398\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+3\beta q^{5}+6q^{13}+5\beta q^{17}-13q^{25}+\cdots\)
2304.2.c.f \(2\) \(18.398\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}+6q^{13}+3\beta q^{17}+3q^{25}+\cdots\)
2304.2.c.g \(2\) \(18.398\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}+2\beta q^{7}+4q^{11}-2q^{13}+\beta q^{17}+\cdots\)
2304.2.c.h \(2\) \(18.398\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}+2\beta q^{7}+4q^{11}+2q^{13}-\beta q^{17}+\cdots\)
2304.2.c.i \(8\) \(18.398\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{5}+\zeta_{24}^{3}q^{7}+\zeta_{24}^{6}q^{11}+\cdots\)
2304.2.c.j \(8\) \(18.398\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{3}q^{5}-\zeta_{24}q^{7}+\zeta_{24}^{6}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)