Properties

Label 3900.2.eu
Level $3900$
Weight $2$
Character orbit 3900.eu
Rep. character $\chi_{3900}(491,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $6656$
Sturm bound $1680$

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Defining parameters

Level: \( N \) \(=\) \( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3900.eu (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3900 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3900, [\chi])\).

Total New Old
Modular forms 6784 6784 0
Cusp forms 6656 6656 0
Eisenstein series 128 128 0

Trace form

\( 6656 q - 6 q^{4} - 9 q^{6} - 6 q^{9} + O(q^{10}) \) \( 6656 q - 6 q^{4} - 9 q^{6} - 6 q^{9} - 24 q^{13} + 6 q^{16} + 18 q^{22} - 42 q^{24} - 64 q^{25} - 18 q^{28} + 11 q^{30} - 18 q^{33} - 19 q^{36} - 108 q^{37} + 20 q^{40} + 43 q^{42} + 6 q^{45} - 78 q^{46} + 48 q^{48} - 3168 q^{49} - 58 q^{52} + 120 q^{54} + 90 q^{58} + 4 q^{61} + 24 q^{64} + 16 q^{66} - 30 q^{69} + 39 q^{72} - 48 q^{76} - 18 q^{78} + 18 q^{81} - 40 q^{82} + 30 q^{84} + 12 q^{85} - 58 q^{88} - 208 q^{90} - 12 q^{93} - 98 q^{94} - 36 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3900, [\chi])\) into newform subspaces

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