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Properties

Label 3900.2.ep
Level $3900$
Weight $2$
Character orbit 3900.ep
Rep. character $\chi_{3900}(697,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $560$
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.ep (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
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 6816 560 6256
Cusp forms 6624 560 6064
Eisenstein series 192 0 192

Trace form

\( 560 q + 4 q^{5} + O(q^{10}) \) \( 560 q + 4 q^{5} - 4 q^{15} - 4 q^{17} - 20 q^{19} - 8 q^{23} + 12 q^{25} + 40 q^{29} - 20 q^{33} - 24 q^{37} - 80 q^{41} + 16 q^{43} + 24 q^{47} + 560 q^{49} - 36 q^{53} - 40 q^{55} - 24 q^{65} - 80 q^{73} - 48 q^{77} + 140 q^{81} + 24 q^{83} + 32 q^{85} + 24 q^{87} + 20 q^{89} + 60 q^{91} + 32 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1950, [\chi])\)\(^{\oplus 2}\)