Properties

Label 3549.2.bz
Level $3549$
Weight $2$
Character orbit 3549.bz
Rep. character $\chi_{3549}(577,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $824$
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.bz (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 2056 824 1232
Cusp forms 1832 824 1008
Eisenstein series 224 0 224

Trace form

\( 824q + 2q^{7} + 412q^{9} + O(q^{10}) \) \( 824q + 2q^{7} + 412q^{9} - 8q^{11} + 80q^{14} + 424q^{16} + 30q^{19} - 8q^{21} + 32q^{22} + 36q^{24} - 16q^{28} + 64q^{29} + 6q^{31} - 20q^{32} - 16q^{35} - 14q^{37} - 120q^{40} - 24q^{42} - 8q^{44} + 16q^{46} + 136q^{50} + 32q^{53} + 12q^{57} + 48q^{58} - 96q^{59} + 44q^{60} - 144q^{61} - 2q^{63} + 2q^{67} - 144q^{68} + 104q^{70} + 72q^{71} + 54q^{73} - 80q^{74} + 12q^{80} - 412q^{81} - 20q^{84} - 88q^{85} - 24q^{86} - 72q^{87} - 48q^{89} + 16q^{92} - 6q^{93} - 24q^{94} - 132q^{96} - 96q^{98} - 16q^{99} + O(q^{100}) \)

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

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