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Properties

Label 3100.3.en
Level $3100$
Weight $3$
Character orbit 3100.en
Rep. character $\chi_{3100}(141,\cdot)$
Character field $\Q(\zeta_{30})$
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.en (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 1280 q - 3 q^{5} - 32 q^{7} - 460 q^{9} + O(q^{10}) \) \( 1280 q - 3 q^{5} - 32 q^{7} - 460 q^{9} - 105 q^{25} + 90 q^{27} + 10 q^{31} - 40 q^{33} + 214 q^{35} + 2 q^{37} + 105 q^{41} + 72 q^{43} - 176 q^{45} + 157 q^{47} + 960 q^{49} + 245 q^{51} + 62 q^{53} - 501 q^{55} + 288 q^{57} - 310 q^{59} - 20 q^{63} + 467 q^{65} - 66 q^{67} + 225 q^{69} + 255 q^{71} - 284 q^{73} - 724 q^{75} + 140 q^{77} - 200 q^{79} + 1345 q^{81} + 870 q^{83} - 330 q^{85} + 450 q^{87} - 75 q^{89} + 183 q^{93} + 229 q^{95} + 345 q^{97} + 840 q^{99} + O(q^{100}) \)

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

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