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Properties

Label 3381.2.bl
Level $3381$
Weight $2$
Character orbit 3381.bl
Rep. character $\chi_{3381}(137,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $5328$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3381.bl (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3381 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3381, [\chi])\).

Total New Old
Modular forms 5424 5424 0
Cusp forms 5328 5328 0
Eisenstein series 96 96 0

Trace form

\( 5328 q - 26 q^{3} - 492 q^{4} - 32 q^{6} - 58 q^{9} + O(q^{10}) \) \( 5328 q - 26 q^{3} - 492 q^{4} - 32 q^{6} - 58 q^{9} - 42 q^{12} - 40 q^{13} + 372 q^{16} - 12 q^{18} - 4 q^{24} + 376 q^{25} - 50 q^{27} - 24 q^{31} - 36 q^{36} - 8 q^{39} - 184 q^{46} - 196 q^{48} - 120 q^{49} + 20 q^{52} - 26 q^{54} + 96 q^{55} - 148 q^{58} + 776 q^{64} - 78 q^{69} + 152 q^{70} + 18 q^{72} - 76 q^{73} - 48 q^{75} - 52 q^{78} + 310 q^{81} - 276 q^{82} - 48 q^{85} - 74 q^{87} - 390 q^{93} + 300 q^{94} + 432 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3381, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.