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Properties

Label 3100.3.cq
Level $3100$
Weight $3$
Character orbit 3100.cq
Rep. character $\chi_{3100}(243,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2288$
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.cq (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 620 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 3888 2320 1568
Cusp forms 3792 2288 1504
Eisenstein series 96 32 64

Trace form

\( 2288 q + 8 q^{2} + 60 q^{6} - 4 q^{8} + O(q^{10}) \) \( 2288 q + 8 q^{2} + 60 q^{6} - 4 q^{8} + 60 q^{12} + 12 q^{13} - 32 q^{16} + 12 q^{17} - 42 q^{18} - 24 q^{21} + 72 q^{22} - 12 q^{26} - 20 q^{28} - 12 q^{32} + 40 q^{33} - 36 q^{36} + 12 q^{37} - 70 q^{38} - 8 q^{41} - 390 q^{42} - 48 q^{48} + 72 q^{52} + 444 q^{53} + 540 q^{56} + 12 q^{57} + 74 q^{62} - 1296 q^{66} - 156 q^{68} - 490 q^{72} + 12 q^{73} - 212 q^{76} + 148 q^{78} + 9712 q^{81} + 220 q^{82} + 804 q^{86} - 378 q^{88} - 460 q^{93} + 276 q^{96} - 144 q^{97} - 74 q^{98} + O(q^{100}) \)

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

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