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Properties

Label 3100.3.gf
Level $3100$
Weight $3$
Character orbit 3100.gf
Rep. character $\chi_{3100}(43,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $9152$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3100.gf (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 620 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3100, [\chi])\).

Total New Old
Modular forms 15552 9280 6272
Cusp forms 15168 9152 6016
Eisenstein series 384 128 256

Trace form

\( 9152 q + 12 q^{2} - 120 q^{6} + 24 q^{8} + O(q^{10}) \) \( 9152 q + 12 q^{2} - 120 q^{6} + 24 q^{8} - 40 q^{12} + 28 q^{13} - 8 q^{16} + 28 q^{17} - 28 q^{18} - 56 q^{21} + 98 q^{22} - 48 q^{26} + 40 q^{28} + 52 q^{32} + 16 q^{36} + 48 q^{37} + 90 q^{38} - 72 q^{41} + 50 q^{42} - 1160 q^{46} + 68 q^{48} + 218 q^{52} - 404 q^{53} - 560 q^{56} + 48 q^{57} + 20 q^{58} - 54 q^{62} + 1976 q^{66} + 186 q^{68} - 1840 q^{72} + 28 q^{73} + 852 q^{76} + 40 q^{77} + 142 q^{78} - 9792 q^{81} - 200 q^{82} - 844 q^{86} + 408 q^{88} + 20 q^{93} - 3956 q^{96} + 184 q^{97} - 486 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(3100, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(3100, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3100, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(620, [\chi])\)\(^{\oplus 2}\)