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Properties

Label 3381.2.r
Level $3381$
Weight $2$
Character orbit 3381.r
Rep. character $\chi_{3381}(883,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $1640$
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.r (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 4640 1640 3000
Cusp forms 4320 1640 2680
Eisenstein series 320 0 320

Trace form

\( 1640 q + 4 q^{2} - 164 q^{4} + 4 q^{5} - 4 q^{6} + 12 q^{8} - 164 q^{9} + O(q^{10}) \) \( 1640 q + 4 q^{2} - 164 q^{4} + 4 q^{5} - 4 q^{6} + 12 q^{8} - 164 q^{9} + 16 q^{11} - 8 q^{13} - 8 q^{15} - 208 q^{16} + 18 q^{17} + 4 q^{18} + 22 q^{19} - 92 q^{20} + 36 q^{22} - 36 q^{23} - 12 q^{24} - 192 q^{25} + 44 q^{26} + 46 q^{29} + 20 q^{30} - 2 q^{31} - 16 q^{32} + 38 q^{34} - 186 q^{36} - 20 q^{37} - 90 q^{38} + 36 q^{39} + 38 q^{40} + 60 q^{41} - 12 q^{43} - 82 q^{44} + 4 q^{45} + 116 q^{46} + 56 q^{47} + 88 q^{48} - 102 q^{50} - 44 q^{51} - 102 q^{52} + 56 q^{53} + 18 q^{54} + 58 q^{55} - 40 q^{57} - 58 q^{58} - 44 q^{59} + 14 q^{60} - 52 q^{61} - 76 q^{64} + 48 q^{65} - 24 q^{66} + 22 q^{67} - 20 q^{68} - 4 q^{69} - 16 q^{71} + 12 q^{72} + 14 q^{73} - 38 q^{74} + 8 q^{75} + 118 q^{76} + 16 q^{78} - 4 q^{79} - 234 q^{80} - 164 q^{81} + 96 q^{82} + 72 q^{83} - 126 q^{85} + 48 q^{86} - 8 q^{87} + 612 q^{88} + 136 q^{89} - 254 q^{92} + 8 q^{93} - 190 q^{94} - 198 q^{95} + 16 q^{96} + 140 q^{97} - 6 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1127, [\chi])\)\(^{\oplus 2}\)