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Properties

Label 3900.2.ea
Level $3900$
Weight $2$
Character orbit 3900.ea
Rep. character $\chi_{3900}(103,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3360$
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.ea (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1300 \)
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 3360 3424
Cusp forms 6656 3360 3296
Eisenstein series 128 0 128

Trace form

\( 3360 q + O(q^{10}) \) \( 3360 q - 8 q^{10} - 8 q^{12} - 4 q^{13} - 40 q^{17} - 32 q^{22} + 40 q^{25} + 8 q^{30} + 128 q^{40} + 40 q^{42} - 124 q^{52} - 8 q^{53} - 232 q^{62} - 20 q^{65} + 24 q^{78} + 840 q^{81} + 8 q^{82} + 184 q^{88} + 32 q^{92} + 40 q^{94} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1300, [\chi])\)\(^{\oplus 2}\)