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Properties

Label 3900.2.ez
Level $3900$
Weight $2$
Character orbit 3900.ez
Rep. character $\chi_{3900}(121,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $576$
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.ez (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
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 6816 576 6240
Cusp forms 6624 576 6048
Eisenstein series 192 0 192

Trace form

\( 576 q + 72 q^{9} + O(q^{10}) \) \( 576 q + 72 q^{9} - 8 q^{13} - 6 q^{15} + 12 q^{23} - 8 q^{25} - 4 q^{29} - 18 q^{33} + 10 q^{35} - 78 q^{41} - 4 q^{43} + 352 q^{49} - 64 q^{51} - 30 q^{55} - 36 q^{59} + 16 q^{61} - 56 q^{65} - 72 q^{67} - 12 q^{69} - 8 q^{75} - 48 q^{77} - 16 q^{79} + 72 q^{81} + 54 q^{85} - 64 q^{91} - 12 q^{95} - 108 q^{97} + O(q^{100}) \)

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.

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

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