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Properties

Label 3381.2.bh
Level $3381$
Weight $2$
Character orbit 3381.bh
Rep. character $\chi_{3381}(361,\cdot)$
Character field $\Q(\zeta_{33})$
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.bh (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{33})\)
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

\( 3200 q - 8 q^{2} + 152 q^{4} + 4 q^{5} + 48 q^{8} + 160 q^{9} + O(q^{10}) \) \( 3200 q - 8 q^{2} + 152 q^{4} + 4 q^{5} + 48 q^{8} + 160 q^{9} - 8 q^{10} - 4 q^{11} + 224 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} + 144 q^{20} + 64 q^{22} + 80 q^{23} + 220 q^{25} + 28 q^{26} + 88 q^{29} + 4 q^{31} + 52 q^{32} - 8 q^{33} - 16 q^{34} - 392 q^{36} + 48 q^{37} + 196 q^{38} - 36 q^{40} - 32 q^{41} - 120 q^{43} + 252 q^{44} + 4 q^{45} - 24 q^{46} + 4 q^{47} - 32 q^{48} - 608 q^{50} + 80 q^{51} + 216 q^{52} - 48 q^{53} - 32 q^{55} - 144 q^{57} - 8 q^{58} + 92 q^{59} + 20 q^{60} + 52 q^{61} + 96 q^{62} - 112 q^{64} + 32 q^{65} - 16 q^{66} - 16 q^{67} - 12 q^{68} - 16 q^{69} - 24 q^{72} + 24 q^{73} - 12 q^{74} + 16 q^{75} + 32 q^{76} + 16 q^{78} - 68 q^{79} - 122 q^{80} + 160 q^{81} + 152 q^{82} + 80 q^{83} + 432 q^{85} + 72 q^{86} + 12 q^{87} - 532 q^{88} - 32 q^{89} + 16 q^{90} + 284 q^{92} - 48 q^{93} - 194 q^{94} + 270 q^{95} + 20 q^{96} + 16 q^{97} + 52 q^{99} + O(q^{100}) \)

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

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