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Properties

Label 3381.2.bd
Level $3381$
Weight $2$
Character orbit 3381.bd
Rep. character $\chi_{3381}(638,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $3180$
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.bd (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 4640 3380 1260
Cusp forms 4320 3180 1140
Eisenstein series 320 200 120

Trace form

\( 3180 q + 7 q^{3} + 330 q^{4} + 20 q^{6} + 15 q^{9} + O(q^{10}) \) \( 3180 q + 7 q^{3} + 330 q^{4} + 20 q^{6} + 15 q^{9} + 22 q^{10} + 18 q^{12} + 14 q^{13} - 44 q^{15} - 250 q^{16} - 42 q^{18} + 22 q^{19} + 70 q^{24} - 252 q^{25} - 26 q^{27} - 33 q^{30} + 14 q^{31} + 22 q^{33} + 44 q^{34} - 86 q^{36} - 22 q^{37} - 21 q^{39} + 176 q^{40} - 154 q^{43} + 102 q^{46} - 40 q^{48} + 11 q^{51} - 66 q^{52} + 5 q^{54} + 44 q^{55} - 88 q^{57} - 76 q^{58} - 99 q^{60} + 66 q^{61} + 84 q^{64} - 110 q^{66} - 36 q^{69} + 213 q^{72} + 40 q^{73} + 52 q^{75} - 66 q^{76} - 104 q^{78} + 66 q^{79} - 161 q^{81} + 112 q^{82} - 116 q^{85} - 101 q^{87} - 66 q^{88} + 242 q^{90} + 116 q^{93} - 112 q^{94} + 327 q^{96} + 88 q^{97} - 187 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)