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Properties

Label 3900.2.eo
Level $3900$
Weight $2$
Character orbit 3900.eo
Rep. character $\chi_{3900}(203,\cdot)$
Character field $\Q(\zeta_{20})$
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.eo (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3900 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 6656 q - 6 q^{6} - 40 q^{9} + O(q^{10}) \) \( 6656 q - 6 q^{6} - 40 q^{9} - 16 q^{10} - 32 q^{13} - 24 q^{16} - 72 q^{21} - 40 q^{22} + 12 q^{24} - 100 q^{28} + 8 q^{30} + 12 q^{33} - 36 q^{34} - 120 q^{37} + 16 q^{40} - 28 q^{42} + 4 q^{45} - 12 q^{46} - 28 q^{48} + 6272 q^{49} - 80 q^{52} + 128 q^{54} - 40 q^{57} - 140 q^{58} + 6 q^{60} - 48 q^{61} - 12 q^{66} - 56 q^{70} - 10 q^{72} - 24 q^{73} - 64 q^{76} - 106 q^{78} - 24 q^{81} - 48 q^{82} - 40 q^{84} - 8 q^{85} + 120 q^{88} - 88 q^{90} - 320 q^{94} - 36 q^{96} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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