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Properties

Label 3100.3.el
Level $3100$
Weight $3$
Character orbit 3100.el
Rep. character $\chi_{3100}(261,\cdot)$
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.el (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

\( 1280 q + 5 q^{3} - 3 q^{5} + 8 q^{7} - 485 q^{9} + O(q^{10}) \) \( 1280 q + 5 q^{3} - 3 q^{5} + 8 q^{7} - 485 q^{9} - 120 q^{15} + 45 q^{23} - 15 q^{25} - 190 q^{27} + 10 q^{31} - 110 q^{33} - 46 q^{35} + 2 q^{37} + 30 q^{41} + 162 q^{43} + 4 q^{45} - 188 q^{47} + 1160 q^{49} + 320 q^{51} - 108 q^{53} - 66 q^{55} - 432 q^{57} - 160 q^{59} - 20 q^{63} + 402 q^{65} - 336 q^{67} + 100 q^{69} + 30 q^{71} - 4 q^{73} - 259 q^{75} + 150 q^{79} + 1520 q^{81} + 290 q^{83} - 75 q^{85} - 660 q^{87} + 408 q^{93} - 326 q^{95} - 115 q^{97} - 1260 q^{99} + O(q^{100}) \)

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

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