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Properties

Label 3381.2.n
Level $3381$
Weight $2$
Character orbit 3381.n
Rep. character $\chi_{3381}(668,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $588$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 928 588 340
Cusp forms 864 588 276
Eisenstein series 64 0 64

Trace form

\( 588 q + 296 q^{4} + 8 q^{9} + O(q^{10}) \) \( 588 q + 296 q^{4} + 8 q^{9} + 12 q^{10} + 30 q^{12} - 28 q^{15} - 300 q^{16} + 10 q^{18} - 6 q^{19} + 16 q^{22} - 286 q^{25} + 52 q^{30} + 42 q^{31} + 30 q^{33} - 16 q^{36} + 30 q^{37} + 34 q^{39} + 36 q^{40} - 76 q^{43} - 30 q^{45} - 32 q^{51} - 48 q^{52} + 54 q^{54} + 44 q^{57} - 76 q^{58} - 68 q^{60} - 36 q^{61} - 496 q^{64} - 38 q^{67} - 82 q^{72} - 18 q^{73} - 78 q^{75} + 20 q^{78} - 62 q^{79} + 48 q^{81} + 80 q^{85} + 30 q^{87} + 60 q^{88} - 60 q^{94} - 84 q^{96} - 240 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)