Properties

Label 2352.2.b
Level $2352$
Weight $2$
Character orbit 2352.b
Rep. character $\chi_{2352}(1567,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $12$
Sturm bound $896$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(896\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

Total New Old
Modular forms 496 40 456
Cusp forms 400 40 360
Eisenstein series 96 0 96

Trace form

\( 40q + 40q^{9} + O(q^{10}) \) \( 40q + 40q^{9} - 64q^{25} - 8q^{37} + 48q^{53} - 8q^{57} + 48q^{65} + 40q^{81} - 40q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2352.2.b.a \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-2\zeta_{6}q^{5}+q^{9}-2\zeta_{6}q^{11}+3\zeta_{6}q^{13}+\cdots\)
2352.2.b.b \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-\zeta_{6}q^{5}+q^{9}-3\zeta_{6}q^{11}-4\zeta_{6}q^{13}+\cdots\)
2352.2.b.c \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-\zeta_{6}q^{5}+q^{9}-\zeta_{6}q^{11}+\zeta_{6}q^{15}+\cdots\)
2352.2.b.d \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-2\zeta_{6}q^{5}+q^{9}+2\zeta_{6}q^{11}+\zeta_{6}q^{13}+\cdots\)
2352.2.b.e \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-2\zeta_{6}q^{5}+q^{9}-2\zeta_{6}q^{11}+\zeta_{6}q^{13}+\cdots\)
2352.2.b.f \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-\zeta_{6}q^{5}+q^{9}+3\zeta_{6}q^{11}-4\zeta_{6}q^{13}+\cdots\)
2352.2.b.g \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-\zeta_{6}q^{5}+q^{9}+\zeta_{6}q^{11}-\zeta_{6}q^{15}+\cdots\)
2352.2.b.h \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-2\zeta_{6}q^{5}+q^{9}+2\zeta_{6}q^{11}+3\zeta_{6}q^{13}+\cdots\)
2352.2.b.i \(4\) \(18.781\) 4.0.2048.2 None \(0\) \(-4\) \(0\) \(0\) \(q-q^{3}+\beta _{1}q^{5}+q^{9}+(2\beta _{1}-2\beta _{3})q^{11}+\cdots\)
2352.2.b.j \(4\) \(18.781\) 4.0.2048.2 None \(0\) \(4\) \(0\) \(0\) \(q+q^{3}+\beta _{1}q^{5}+q^{9}+(-2\beta _{1}+2\beta _{3})q^{11}+\cdots\)
2352.2.b.k \(8\) \(18.781\) 8.0.339738624.1 None \(0\) \(-8\) \(0\) \(0\) \(q-q^{3}+(-\beta _{4}+\beta _{6})q^{5}+q^{9}+(\beta _{2}+\beta _{4}+\cdots)q^{11}+\cdots\)
2352.2.b.l \(8\) \(18.781\) 8.0.339738624.1 None \(0\) \(8\) \(0\) \(0\) \(q+q^{3}+(-\beta _{4}+\beta _{6})q^{5}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)