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Properties

Label 3381.2.bk
Level $3381$
Weight $2$
Character orbit 3381.bk
Rep. character $\chi_{3381}(47,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $4920$
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.bk (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
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 4920 504
Cusp forms 5328 4920 408
Eisenstein series 96 0 96

Trace form

\( 4920 q - 408 q^{4} + 10 q^{7} + O(q^{10}) \) \( 4920 q - 408 q^{4} + 10 q^{7} + 12 q^{10} - 40 q^{12} - 12 q^{15} + 404 q^{16} + 10 q^{18} - 6 q^{19} + 6 q^{21} + 44 q^{22} + 418 q^{25} + 68 q^{28} + 12 q^{30} + 42 q^{31} + 30 q^{33} + 16 q^{37} + 10 q^{39} - 132 q^{40} + 66 q^{42} - 20 q^{43} + 12 q^{45} + 22 q^{49} + 8 q^{51} - 104 q^{52} + 54 q^{54} - 196 q^{55} + 2 q^{57} - 224 q^{58} + 200 q^{60} + 62 q^{61} + 38 q^{63} + 816 q^{64} + 196 q^{66} - 10 q^{67} + 48 q^{70} - 42 q^{72} - 18 q^{73} + 174 q^{75} + 336 q^{76} - 44 q^{78} + 14 q^{79} + 8 q^{81} - 172 q^{84} + 40 q^{85} - 194 q^{87} + 12 q^{88} - 448 q^{90} + 118 q^{91} - 60 q^{94} - 336 q^{96} + 192 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3381, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)