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Properties

Label 3381.2.ba
Level $3381$
Weight $2$
Character orbit 3381.ba
Rep. character $\chi_{3381}(97,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1600$
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.ba (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
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 1600 3040
Cusp forms 4320 1600 2720
Eisenstein series 320 0 320

Trace form

\( 1600 q - 8 q^{2} - 152 q^{4} - 24 q^{8} + 160 q^{9} + O(q^{10}) \) \( 1600 q - 8 q^{2} - 152 q^{4} - 24 q^{8} + 160 q^{9} - 224 q^{16} + 8 q^{18} - 88 q^{23} - 96 q^{25} + 8 q^{29} - 8 q^{32} + 196 q^{36} + 88 q^{37} + 88 q^{43} + 308 q^{44} - 48 q^{46} + 292 q^{50} + 88 q^{51} + 88 q^{57} + 84 q^{58} - 56 q^{64} + 48 q^{71} + 24 q^{72} - 44 q^{74} + 88 q^{79} - 160 q^{81} + 288 q^{85} + 572 q^{88} + 356 q^{92} - 48 q^{93} - 300 q^{95} - 44 q^{99} + O(q^{100}) \)

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

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