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Properties

Label 3100.3.bh
Level $3100$
Weight $3$
Character orbit 3100.bh
Rep. character $\chi_{3100}(1399,\cdot)$
Character field $\Q(\zeta_{10})$
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.bh (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 620 \)
Character field: \(\Q(\zeta_{10})\)
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

\( 2288 q + 14 q^{4} - 56 q^{6} - 1680 q^{9} + O(q^{10}) \) \( 2288 q + 14 q^{4} - 56 q^{6} - 1680 q^{9} + 36 q^{14} + 98 q^{16} - 84 q^{21} + 114 q^{24} - 212 q^{26} + 12 q^{29} + 262 q^{34} + 308 q^{36} - 12 q^{41} + 194 q^{44} + 418 q^{46} - 3584 q^{49} + 650 q^{54} - 972 q^{56} + 96 q^{61} - 256 q^{64} + 248 q^{66} - 12 q^{69} - 804 q^{74} + 318 q^{76} - 4944 q^{81} + 1098 q^{84} - 650 q^{86} + 12 q^{89} - 364 q^{94} + 1044 q^{96} + O(q^{100}) \)

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

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