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Properties

Label 2624.2.l
Level $2624$
Weight $2$
Character orbit 2624.l
Rep. character $\chi_{2624}(2305,\cdot)$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
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 696 172 524
Cusp forms 648 164 484
Eisenstein series 48 8 40

Trace form

\( 164 q + O(q^{10}) \) \( 164 q + 4 q^{13} + 4 q^{17} - 172 q^{25} + 4 q^{29} + 8 q^{37} + 4 q^{41} - 32 q^{45} + 4 q^{53} - 40 q^{57} + 16 q^{65} + 16 q^{69} - 44 q^{81} - 16 q^{85} - 28 q^{89} - 32 q^{93} + 4 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(328, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(656, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1312, [\chi])\)\(^{\oplus 2}\)