Properties

Label 624.1.cb
Level $624$
Weight $1$
Character orbit 624.cb
Rep. character $\chi_{624}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 624.cb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(624, [\chi])\).

Total New Old
Modular forms 32 6 26
Cusp forms 8 2 6
Eisenstein series 24 4 20

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q - q^{3} + 3 q^{7} - q^{9} + O(q^{10}) \) \( 2 q - q^{3} + 3 q^{7} - q^{9} + q^{13} - 2 q^{25} + 2 q^{27} - 2 q^{39} - q^{43} + 2 q^{49} - q^{61} - 3 q^{63} - 3 q^{67} + q^{75} - 2 q^{79} - q^{81} + 3 q^{91} - 3 q^{93} - 3 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(624, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
624.1.cb.a \(2\) \(0.311\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(3\) \(q-\zeta_{6}q^{3}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(624, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)