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Properties

Label 3381.2.bz
Level $3381$
Weight $2$
Character orbit 3381.bz
Rep. character $\chi_{3381}(41,\cdot)$
Character field $\Q(\zeta_{154})$
Dimension $26640$
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.bz (of order \(154\) and degree \(60\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3381 \)
Character field: \(\Q(\zeta_{154})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 27120 27120 0
Cusp forms 26640 26640 0
Eisenstein series 480 480 0

Trace form

\( 26640 q - 63 q^{3} - 530 q^{4} - 91 q^{6} - 108 q^{7} - 65 q^{9} + O(q^{10}) \) \( 26640 q - 63 q^{3} - 530 q^{4} - 91 q^{6} - 108 q^{7} - 65 q^{9} - 126 q^{10} - 63 q^{12} - 126 q^{13} - 57 q^{15} + 358 q^{16} - 116 q^{18} - 13 q^{21} - 184 q^{22} - 140 q^{24} + 338 q^{25} - 252 q^{27} - 100 q^{28} - 116 q^{30} - 63 q^{33} - 14 q^{34} + 19 q^{36} - 106 q^{37} - 57 q^{39} - 14 q^{40} + 16 q^{42} - 122 q^{43} - 140 q^{45} - 172 q^{46} - 256 q^{49} - 69 q^{51} - 126 q^{52} - 63 q^{54} - 238 q^{55} - 55 q^{57} + 138 q^{58} - 89 q^{60} - 126 q^{61} - 19 q^{63} - 522 q^{64} + 77 q^{66} - 184 q^{67} + 14 q^{69} - 48 q^{70} - 181 q^{72} - 126 q^{73} - 63 q^{75} - 238 q^{76} - 475 q^{78} - 288 q^{79} + 71 q^{81} + 14 q^{82} + 24 q^{84} - 162 q^{85} - 63 q^{87} + 86 q^{88} - 133 q^{90} - 32 q^{91} - 216 q^{93} - 70 q^{94} - 273 q^{96} + 124 q^{99} + O(q^{100}) \)

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.