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Properties

Label 2624.2.bp
Level $2624$
Weight $2$
Character orbit 2624.bp
Rep. character $\chi_{2624}(495,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $328$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2624 = 2^{6} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2624.bp (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 656 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1376 344 1032
Cusp forms 1312 328 984
Eisenstein series 64 16 48

Trace form

\( 328 q + 4 q^{3} - 8 q^{5} + 8 q^{7} + O(q^{10}) \) \( 328 q + 4 q^{3} - 8 q^{5} + 8 q^{7} + 4 q^{11} - 4 q^{13} + 24 q^{15} - 8 q^{17} + 4 q^{19} - 8 q^{21} + 296 q^{25} - 8 q^{27} - 4 q^{29} - 8 q^{33} + 48 q^{35} - 8 q^{37} + 8 q^{39} + 8 q^{43} - 40 q^{45} - 48 q^{47} - 8 q^{49} + 8 q^{51} - 4 q^{53} + 8 q^{55} - 40 q^{59} - 8 q^{61} + 24 q^{63} - 8 q^{65} - 20 q^{67} + 8 q^{69} + 8 q^{71} + 4 q^{75} - 8 q^{77} + 8 q^{83} - 24 q^{85} + 8 q^{87} - 16 q^{89} + 32 q^{93} + 40 q^{95} - 8 q^{97} - 44 q^{99} + O(q^{100}) \)

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

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