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Properties

Label 2624.2.cf
Level $2624$
Weight $2$
Character orbit 2624.cf
Rep. character $\chi_{2624}(165,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2560$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2624 = 2^{6} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2624.cf (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2704 2560 144
Cusp forms 2672 2560 112
Eisenstein series 32 0 32

Trace form

\( 2560 q + O(q^{10}) \) \( 2560 q - 16 q^{22} - 80 q^{24} - 80 q^{26} - 80 q^{40} - 80 q^{42} - 16 q^{44} - 64 q^{51} + 128 q^{54} + 112 q^{56} - 128 q^{59} + 192 q^{60} - 160 q^{63} - 160 q^{67} + 192 q^{70} - 128 q^{71} + 112 q^{74} + 128 q^{76} - 64 q^{79} - 128 q^{80} - 208 q^{86} - 288 q^{90} - 192 q^{94} - 272 q^{96} - 272 q^{98} + O(q^{100}) \)

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

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