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Properties

Label 3900.2.fh
Level $3900$
Weight $2$
Character orbit 3900.fh
Rep. character $\chi_{3900}(37,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1120$
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.fh (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 13632 1120 12512
Cusp forms 13248 1120 12128
Eisenstein series 384 0 384

Trace form

\( 1120 q - 4 q^{5} + O(q^{10}) \) \( 1120 q - 4 q^{5} + 12 q^{13} + 4 q^{15} - 8 q^{17} + 20 q^{19} + 8 q^{23} + 12 q^{25} - 40 q^{29} + 8 q^{33} + 24 q^{37} - 100 q^{41} - 4 q^{43} - 24 q^{47} - 560 q^{49} + 12 q^{53} + 124 q^{55} - 84 q^{65} - 72 q^{67} - 160 q^{73} + 48 q^{77} - 140 q^{81} - 24 q^{83} - 44 q^{85} + 36 q^{87} - 20 q^{89} + 120 q^{91} + 64 q^{95} - 36 q^{97} + O(q^{100}) \)

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

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