Properties

Label 3549.2.dg
Level $3549$
Weight $2$
Character orbit 3549.dg
Rep. character $\chi_{3549}(25,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $5808$
Sturm bound $970$

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Defining parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.dg (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1183 \)
Character field: \(\Q(\zeta_{78})\)
Sturm bound: \(970\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3549, [\chi])\).

Total New Old
Modular forms 11760 5808 5952
Cusp forms 11568 5808 5760
Eisenstein series 192 0 192

Trace form

\( 5808q - 2q^{3} - 240q^{4} + 242q^{9} + O(q^{10}) \) \( 5808q - 2q^{3} - 240q^{4} + 242q^{9} + 8q^{10} + 4q^{12} + 72q^{13} - 40q^{14} + 252q^{16} - 24q^{22} - 238q^{25} - 22q^{26} + 4q^{27} + 130q^{32} + 32q^{35} + 480q^{36} - 220q^{38} + q^{39} - 44q^{40} + 122q^{42} + 4q^{43} + 16q^{48} - 246q^{49} + 8q^{51} - 38q^{52} + 176q^{53} + 88q^{55} - 96q^{56} + 52q^{58} - 208q^{59} - 32q^{61} + 192q^{62} + 592q^{64} - 26q^{65} - 16q^{66} + 156q^{67} - 110q^{68} - 32q^{69} + 156q^{71} - 184q^{74} + 30q^{75} + 312q^{76} + 12q^{77} - 60q^{78} + 10q^{79} + 242q^{81} + 416q^{85} + 156q^{86} - 36q^{87} - 16q^{90} - 131q^{91} - 39q^{93} + 78q^{94} + 104q^{95} - 312q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3549, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3549, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)