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Properties

Label 3549.2.ee
Level $3549$
Weight $2$
Character orbit 3549.ee
Rep. character $\chi_{3549}(50,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $17472$
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.ee (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 507 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 23520 17472 6048
Cusp forms 23136 17472 5664
Eisenstein series 384 0 384

Trace form

\( 17472 q + 12 q^{6} + O(q^{10}) \) \( 17472 q + 12 q^{6} + 48 q^{10} + 32 q^{13} - 4 q^{15} - 728 q^{16} + 16 q^{18} + 8 q^{19} + 4 q^{21} - 224 q^{24} - 24 q^{27} + 176 q^{30} - 16 q^{31} - 48 q^{34} - 12 q^{36} - 48 q^{37} + 48 q^{39} - 232 q^{45} - 72 q^{46} - 24 q^{48} + 144 q^{52} + 108 q^{54} + 448 q^{55} + 28 q^{57} + 120 q^{58} + 116 q^{60} + 48 q^{61} - 16 q^{63} - 104 q^{66} + 16 q^{67} - 72 q^{69} - 48 q^{70} - 52 q^{72} + 16 q^{73} - 60 q^{75} - 16 q^{76} + 4 q^{78} + 16 q^{79} - 12 q^{81} + 400 q^{82} - 72 q^{84} + 40 q^{85} + 24 q^{87} - 72 q^{88} - 16 q^{91} - 352 q^{93} + 648 q^{96} - 96 q^{97} + 144 q^{99} + O(q^{100}) \)

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

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