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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

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

Display 100 coefficients 10 coefficients

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

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