Properties

Label 2304.2.l
Level $2304$
Weight $2$
Character orbit 2304.l
Rep. character $\chi_{2304}(575,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $8$
Sturm bound $768$
Trace bound $37$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2304.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 8 \)
Sturm bound: \(768\)
Trace bound: \(37\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(37\)

Dimensions

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

Total New Old
Modular forms 864 64 800
Cusp forms 672 64 608
Eisenstein series 192 0 192

Trace form

\( 64q + O(q^{10}) \) \( 64q + 64q^{49} + O(q^{100}) \)

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.l.a \(8\) \(18.398\) 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{4})q^{5}+(-\beta _{1}+\beta _{7})q^{7}+\cdots\)
2304.2.l.b \(8\) \(18.398\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{6})q^{5}+\zeta_{24}^{6}q^{7}+\cdots\)
2304.2.l.c \(8\) \(18.398\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{6})q^{5}+\zeta_{24}^{6}q^{7}+\cdots\)
2304.2.l.d \(8\) \(18.398\) 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}+\beta _{7})q^{7}+\cdots\)
2304.2.l.e \(8\) \(18.398\) 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{3})q^{5}+(\beta _{1}-\beta _{7})q^{7}+(1+\cdots)q^{11}+\cdots\)
2304.2.l.f \(8\) \(18.398\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{6})q^{5}-\zeta_{24}^{6}q^{7}+\cdots\)
2304.2.l.g \(8\) \(18.398\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{6})q^{5}-\zeta_{24}^{6}q^{7}+\cdots\)
2304.2.l.h \(8\) \(18.398\) 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{4})q^{5}+(\beta _{1}-\beta _{7})q^{7}+(1+\cdots)q^{11}+\cdots\)

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

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