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Properties

Label 3381.2.cf
Level $3381$
Weight $2$
Character orbit 3381.cf
Rep. character $\chi_{3381}(10,\cdot)$
Character field $\Q(\zeta_{462})$
Dimension $26880$
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.cf (of order \(462\) and degree \(120\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1127 \)
Character field: \(\Q(\zeta_{462})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 54240 26880 27360
Cusp forms 53280 26880 26400
Eisenstein series 960 0 960

Trace form

\( 26880 q - 224 q^{4} + 224 q^{9} + O(q^{10}) \) \( 26880 q - 224 q^{4} + 224 q^{9} - 224 q^{16} - 616 q^{20} - 8 q^{23} - 220 q^{25} + 28 q^{26} + 176 q^{28} + 8 q^{29} - 12 q^{31} - 20 q^{32} - 176 q^{35} - 448 q^{36} - 56 q^{41} + 110 q^{42} - 16 q^{46} - 12 q^{47} + 120 q^{49} + 464 q^{50} - 108 q^{52} - 56 q^{55} + 110 q^{56} - 484 q^{58} - 160 q^{59} + 448 q^{64} + 188 q^{70} - 32 q^{71} - 36 q^{73} - 48 q^{75} - 84 q^{77} + 40 q^{78} + 44 q^{79} + 594 q^{80} - 224 q^{81} + 116 q^{82} - 376 q^{85} + 36 q^{87} + 154 q^{88} - 328 q^{92} - 1894 q^{94} + 2 q^{95} + 60 q^{96} - 368 q^{98} + 44 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1127, [\chi])\)\(^{\oplus 2}\)