Properties

Label 2304.2.f
Level $2304$
Weight $2$
Character orbit 2304.f
Rep. character $\chi_{2304}(1151,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $8$
Sturm bound $768$
Trace bound $43$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2304.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(768\)
Trace bound: \(43\)
Distinguishing \(T_p\): \(5\), \(7\), \(23\), \(43\)

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

\( 32 q + O(q^{10}) \) \( 32 q + 32 q^{25} - 96 q^{49} - 64 q^{73} + 64 q^{97} + O(q^{100}) \)

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.f.a \(4\) \(18.398\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-2+\zeta_{8}^{3})q^{5}+(\zeta_{8}-2\zeta_{8}^{2})q^{7}+\cdots\)
2304.2.f.b \(4\) \(18.398\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-2+\zeta_{8}^{3})q^{5}+(-\zeta_{8}+2\zeta_{8}^{2})q^{7}+\cdots\)
2304.2.f.c \(4\) \(18.398\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{5}+2\zeta_{8}q^{7}-4\zeta_{8}^{2}q^{11}-2\zeta_{8}q^{13}+\cdots\)
2304.2.f.d \(4\) \(18.398\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{5}+2\zeta_{8}q^{13}+5\zeta_{8}^{2}q^{17}+\cdots\)
2304.2.f.e \(4\) \(18.398\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{5}+2\zeta_{8}q^{7}-4\zeta_{8}^{2}q^{11}+2\zeta_{8}q^{13}+\cdots\)
2304.2.f.f \(4\) \(18.398\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{5}-2\zeta_{8}q^{13}-\zeta_{8}^{2}q^{17}+13q^{25}+\cdots\)
2304.2.f.g \(4\) \(18.398\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(0\) \(q+(2+\zeta_{8}^{3})q^{5}+(\zeta_{8}+2\zeta_{8}^{2})q^{7}+2\zeta_{8}^{2}q^{11}+\cdots\)
2304.2.f.h \(4\) \(18.398\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(0\) \(q+(2+\zeta_{8}^{3})q^{5}+(\zeta_{8}+2\zeta_{8}^{2})q^{7}+2\zeta_{8}^{2}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)