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Properties

Label 2624.2.da
Level $2624$
Weight $2$
Character orbit 2624.da
Rep. character $\chi_{2624}(49,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $656$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2624 = 2^{6} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2624.da (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 656 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2752 688 2064
Cusp forms 2624 656 1968
Eisenstein series 128 32 96

Trace form

\( 656 q + 16 q^{3} - 10 q^{5} + 624 q^{9} + O(q^{10}) \) \( 656 q + 16 q^{3} - 10 q^{5} + 624 q^{9} + 10 q^{11} - 6 q^{13} + 16 q^{15} - 16 q^{17} + 10 q^{19} - 28 q^{21} + 88 q^{27} - 6 q^{29} - 12 q^{31} - 20 q^{33} - 50 q^{35} - 6 q^{37} + 4 q^{39} + 42 q^{43} - 66 q^{45} + 16 q^{47} - 20 q^{49} + 36 q^{51} - 10 q^{53} + 20 q^{55} - 60 q^{57} + 30 q^{59} - 10 q^{61} + 128 q^{63} - 48 q^{65} + 10 q^{67} - 40 q^{69} - 16 q^{73} + 40 q^{75} - 38 q^{77} + 16 q^{79} + 496 q^{81} + 16 q^{83} + 84 q^{87} - 8 q^{89} - 28 q^{91} + 24 q^{93} - 8 q^{95} - 16 q^{97} + 130 q^{99} + O(q^{100}) \)

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

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