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Properties

Label 2624.2.n
Level $2624$
Weight $2$
Character orbit 2624.n
Rep. character $\chi_{2624}(657,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $160$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2624 = 2^{6} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2624.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 688 160 528
Cusp forms 656 160 496
Eisenstein series 32 0 32

Trace form

\( 160 q + O(q^{10}) \) \( 160 q + 8 q^{11} + 16 q^{15} + 16 q^{19} - 16 q^{29} - 16 q^{37} - 8 q^{43} + 40 q^{47} - 160 q^{49} + 24 q^{51} + 16 q^{53} - 32 q^{59} + 32 q^{61} - 40 q^{63} - 40 q^{67} + 32 q^{69} + 56 q^{75} + 16 q^{77} + 8 q^{79} - 160 q^{81} - 32 q^{85} + 32 q^{91} - 64 q^{95} - 24 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)