Properties

Label 3549.2.cw
Level $3549$
Weight $2$
Character orbit 3549.cw
Rep. character $\chi_{3549}(8,\cdot)$
Character field $\Q(\zeta_{52})$
Dimension $8736$
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.cw (of order \(52\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 507 \)
Character field: \(\Q(\zeta_{52})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 11712 8736 2976
Cusp forms 11520 8736 2784
Eisenstein series 192 0 192

Trace form

\( 8736q - 12q^{6} + O(q^{10}) \) \( 8736q - 12q^{6} - 8q^{13} + 4q^{15} + 728q^{16} + 20q^{18} - 8q^{19} - 4q^{21} + 320q^{24} + 24q^{27} - 104q^{30} + 16q^{31} - 36q^{33} + 48q^{37} - 96q^{39} + 232q^{45} + 24q^{46} - 48q^{48} + 72q^{52} - 36q^{54} - 352q^{55} + 32q^{57} - 24q^{58} - 44q^{60} + 96q^{61} - 8q^{63} + 104q^{66} - 40q^{67} - 24q^{70} - 32q^{72} - 16q^{73} - 104q^{76} + 68q^{78} - 16q^{79} - 24q^{81} - 520q^{82} - 12q^{84} + 32q^{85} + 48q^{87} - 8q^{91} + 280q^{93} - 684q^{96} + 96q^{97} + 12q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)