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Properties

Label 3381.2.be
Level $3381$
Weight $2$
Character orbit 3381.be
Rep. character $\chi_{3381}(146,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $3120$
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.be (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
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 3280 1360
Cusp forms 4320 3120 1200
Eisenstein series 320 160 160

Trace form

\( 3120 q + 340 q^{4} + 26 q^{9} + O(q^{10}) \) \( 3120 q + 340 q^{4} + 26 q^{9} - 32 q^{15} - 204 q^{16} + 58 q^{18} - 128 q^{22} - 228 q^{25} - 98 q^{30} - 28 q^{36} + 92 q^{37} + 22 q^{39} - 32 q^{43} + 12 q^{46} + 14 q^{51} + 28 q^{57} + 140 q^{58} - 10 q^{60} + 104 q^{64} + 116 q^{67} - 134 q^{72} + 20 q^{78} - 100 q^{79} - 206 q^{81} - 120 q^{85} + 180 q^{88} + 16 q^{93} + 196 q^{99} + O(q^{100}) \)

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

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