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Properties

Label 3185.2.et
Level $3185$
Weight $2$
Character orbit 3185.et
Rep. character $\chi_{3185}(372,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $4656$
Sturm bound $784$

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Defining parameters

Level: \( N \) \(=\) \( 3185 = 5 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3185.et (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3185 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(784\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3185, [\chi])\).

Total New Old
Modular forms 4752 4752 0
Cusp forms 4656 4656 0
Eisenstein series 96 96 0

Trace form

\( 4656 q - 20 q^{3} + 768 q^{4} - 10 q^{5} - 20 q^{6} - 24 q^{7} + O(q^{10}) \) \( 4656 q - 20 q^{3} + 768 q^{4} - 10 q^{5} - 20 q^{6} - 24 q^{7} - 16 q^{10} - 28 q^{11} - 16 q^{12} - 10 q^{13} + 2 q^{15} - 792 q^{16} - 40 q^{18} + 8 q^{19} - 2 q^{20} - 16 q^{21} - 20 q^{22} - 40 q^{24} - 20 q^{26} - 68 q^{27} - 16 q^{28} - 16 q^{30} - 64 q^{31} - 56 q^{34} - 12 q^{35} + 4 q^{37} + 40 q^{38} - 68 q^{40} + 4 q^{41} - 48 q^{42} - 116 q^{44} + 32 q^{45} - 28 q^{46} + 40 q^{47} + 8 q^{48} + 24 q^{49} + 184 q^{50} - 6 q^{52} - 20 q^{53} - 76 q^{54} - 80 q^{55} - 36 q^{58} + 12 q^{59} - 70 q^{60} - 56 q^{61} + 136 q^{62} + 688 q^{64} + 34 q^{65} - 40 q^{66} - 16 q^{68} + 16 q^{69} - 106 q^{70} - 100 q^{71} - 252 q^{72} - 56 q^{75} - 140 q^{76} + 20 q^{77} + 22 q^{78} + 12 q^{80} + 672 q^{81} - 16 q^{82} - 160 q^{83} + 36 q^{84} + 74 q^{85} + 36 q^{86} - 60 q^{87} - 80 q^{88} - 8 q^{89} - 116 q^{90} - 56 q^{91} + 12 q^{92} - 220 q^{93} - 160 q^{95} + 240 q^{96} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3185, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.