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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

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

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

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