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Properties

Label 3100.3.dc
Level $3100$
Weight $3$
Character orbit 3100.dc
Rep. character $\chi_{3100}(233,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1280$
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.dc (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 7728 1280 6448
Cusp forms 7632 1280 6352
Eisenstein series 96 0 96

Trace form

\( 1280 q + 6 q^{3} - 24 q^{7} + O(q^{10}) \) \( 1280 q + 6 q^{3} - 24 q^{7} + 24 q^{15} + 28 q^{23} - 84 q^{25} + 90 q^{27} - 102 q^{33} + 198 q^{35} + 144 q^{37} + 168 q^{43} - 138 q^{45} + 234 q^{47} - 200 q^{49} - 160 q^{53} - 280 q^{55} + 402 q^{57} + 250 q^{59} + 164 q^{63} + 514 q^{65} + 84 q^{67} - 120 q^{71} - 88 q^{73} + 428 q^{75} + 332 q^{77} - 1100 q^{79} - 11940 q^{81} + 186 q^{83} - 376 q^{85} + 68 q^{87} + 68 q^{93} + 664 q^{95} - 788 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3100, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1550, [\chi])\)\(^{\oplus 2}\)