Properties

Label 3549.2.bd
Level $3549$
Weight $2$
Character orbit 3549.bd
Rep. character $\chi_{3549}(316,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $304$
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.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 1028 304 724
Cusp forms 916 304 612
Eisenstein series 112 0 112

Trace form

\( 304q + 148q^{4} - 152q^{9} + O(q^{10}) \) \( 304q + 148q^{4} - 152q^{9} + 16q^{10} + 12q^{11} - 32q^{12} + 12q^{15} - 156q^{16} - 8q^{17} - 24q^{20} + 12q^{22} + 12q^{23} - 336q^{25} - 4q^{29} + 8q^{30} - 12q^{33} - 8q^{35} + 148q^{36} - 12q^{37} + 56q^{38} + 136q^{40} + 12q^{41} + 4q^{42} + 16q^{43} + 12q^{45} + 12q^{46} - 16q^{48} + 152q^{49} - 60q^{50} + 24q^{51} - 32q^{53} - 28q^{55} - 12q^{58} + 84q^{59} + 4q^{61} + 28q^{62} - 384q^{64} + 48q^{66} - 12q^{67} - 40q^{68} - 4q^{69} - 48q^{74} + 32q^{75} - 48q^{76} - 16q^{77} - 64q^{79} - 144q^{80} - 152q^{81} + 100q^{82} - 24q^{85} - 32q^{87} - 36q^{88} - 96q^{89} - 32q^{90} + 216q^{92} - 8q^{94} + 48q^{95} + 60q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)