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Properties

Label 2624.2.i
Level $2624$
Weight $2$
Character orbit 2624.i
Rep. character $\chi_{2624}(337,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $164$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2624 = 2^{6} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2624.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 656 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2624, [\chi])\).

Total New Old
Modular forms 688 172 516
Cusp forms 656 164 492
Eisenstein series 32 8 24

Trace form

\( 164 q - 156 q^{9} + O(q^{10}) \) \( 164 q - 156 q^{9} + 4 q^{11} + 4 q^{15} - 4 q^{17} + 4 q^{19} + 12 q^{21} + 32 q^{31} + 48 q^{35} - 4 q^{37} - 56 q^{39} + 32 q^{43} - 24 q^{45} + 4 q^{47} + 4 q^{51} - 4 q^{53} + 20 q^{55} - 20 q^{59} + 32 q^{63} - 12 q^{65} - 20 q^{67} + 8 q^{69} - 16 q^{73} + 4 q^{75} - 28 q^{77} + 4 q^{79} + 124 q^{81} + 4 q^{83} + 16 q^{85} + 24 q^{87} - 8 q^{89} - 28 q^{91} + 28 q^{95} - 4 q^{97} + 28 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2624, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2624, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(656, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1312, [\chi])\)\(^{\oplus 2}\)