↑

Properties

Label 3381.2.bs
Level $3381$
Weight $2$
Character orbit 3381.bs
Rep. character $\chi_{3381}(263,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $6240$
Sturm bound $896$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3381.bs (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 9280 6560 2720
Cusp forms 8640 6240 2400
Eisenstein series 640 320 320

Trace form

\( 6240 q + 9 q^{3} - 286 q^{4} + 20 q^{6} + 13 q^{9} + O(q^{10}) \) \( 6240 q + 9 q^{3} - 286 q^{4} + 20 q^{6} + 13 q^{9} + 22 q^{10} + 25 q^{12} + 72 q^{13} - 88 q^{15} + 282 q^{16} + 105 q^{18} + 22 q^{19} - 2 q^{24} + 314 q^{25} + 90 q^{27} + 99 q^{30} + 18 q^{31} + 11 q^{33} + 88 q^{34} + 110 q^{37} + 7 q^{39} + 22 q^{40} - 352 q^{43} + 18 q^{46} + 228 q^{48} + 11 q^{51} + 166 q^{52} - 35 q^{54} + 160 q^{55} - 88 q^{57} + 206 q^{58} + 11 q^{60} - 66 q^{61} + 256 q^{64} - 22 q^{66} + 22 q^{67} + 24 q^{69} + 97 q^{72} + 42 q^{73} - 123 q^{75} + 88 q^{76} + 104 q^{78} + 66 q^{79} + 181 q^{81} + 14 q^{82} + 48 q^{85} - 75 q^{87} - 66 q^{88} - 60 q^{93} + 146 q^{94} - 5 q^{96} + 88 q^{97} + 176 q^{99} + O(q^{100}) \)

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

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