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Properties

Label 2624.2.df
Level $2624$
Weight $2$
Character orbit 2624.df
Rep. character $\chi_{2624}(15,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $1312$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2624 = 2^{6} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2624.df (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 656 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 5504 1376 4128
Cusp forms 5248 1312 3936
Eisenstein series 256 64 192

Trace form

\( 1312 q + 16 q^{3} - 12 q^{5} + 32 q^{7} + O(q^{10}) \) \( 1312 q + 16 q^{3} - 12 q^{5} + 32 q^{7} + 16 q^{11} - 16 q^{13} - 24 q^{15} - 32 q^{17} + 16 q^{19} - 12 q^{21} + 40 q^{23} - 296 q^{25} + 88 q^{27} - 16 q^{29} - 32 q^{33} - 28 q^{35} - 12 q^{37} + 32 q^{39} + 12 q^{43} - 80 q^{45} + 48 q^{47} - 32 q^{49} + 12 q^{51} - 16 q^{53} + 32 q^{55} + 60 q^{59} - 12 q^{61} - 24 q^{63} - 32 q^{65} + 40 q^{67} - 28 q^{69} + 32 q^{71} + 16 q^{75} - 12 q^{77} + 32 q^{83} + 4 q^{85} + 32 q^{87} + 16 q^{89} - 52 q^{93} - 40 q^{95} - 32 q^{97} - 116 q^{99} + O(q^{100}) \)

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

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