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Properties

Label 3381.2.bv
Level $3381$
Weight $2$
Character orbit 3381.bv
Rep. character $\chi_{3381}(19,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $3200$
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.bv (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
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 3200 6080
Cusp forms 8640 3200 5440
Eisenstein series 640 0 640

Trace form

\( 3200 q + 8 q^{2} + 152 q^{4} - 48 q^{8} - 160 q^{9} + O(q^{10}) \) \( 3200 q + 8 q^{2} + 152 q^{4} - 48 q^{8} - 160 q^{9} + 224 q^{16} - 8 q^{18} + 64 q^{23} + 108 q^{25} + 84 q^{26} + 40 q^{29} - 12 q^{31} - 52 q^{32} + 392 q^{36} - 88 q^{37} + 176 q^{43} - 308 q^{44} - 12 q^{47} + 464 q^{50} - 88 q^{51} - 108 q^{52} + 176 q^{57} - 24 q^{58} + 36 q^{59} - 112 q^{64} - 24 q^{72} + 48 q^{73} + 44 q^{74} - 48 q^{75} - 48 q^{78} + 44 q^{79} + 594 q^{80} + 160 q^{81} - 24 q^{82} - 384 q^{85} + 36 q^{87} - 572 q^{88} - 356 q^{92} + 48 q^{93} + 486 q^{94} + 306 q^{95} + 60 q^{96} + 44 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1127, [\chi])\)\(^{\oplus 2}\)