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Properties

Label 3100.3.ef
Level $3100$
Weight $3$
Character orbit 3100.ef
Rep. character $\chi_{3100}(51,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $4816$
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.ef (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 124 \)
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 7776 4912 2864
Cusp forms 7584 4816 2768
Eisenstein series 192 96 96

Trace form

\( 4816 q + 6 q^{2} + 10 q^{4} - 17 q^{6} - 27 q^{8} - 1752 q^{9} + O(q^{10}) \) \( 4816 q + 6 q^{2} + 10 q^{4} - 17 q^{6} - 27 q^{8} - 1752 q^{9} + 63 q^{12} + 10 q^{13} - 26 q^{14} - 70 q^{16} + 18 q^{17} + 53 q^{18} - 18 q^{21} - 77 q^{22} + 18 q^{24} + 119 q^{26} + 52 q^{28} + 12 q^{29} - 74 q^{32} - 72 q^{33} + 214 q^{34} - 41 q^{36} - 32 q^{37} + 28 q^{38} - 54 q^{41} - 41 q^{42} + 225 q^{44} - 222 q^{46} - 278 q^{48} - 4232 q^{49} - 241 q^{52} - 62 q^{53} - 424 q^{54} + 88 q^{56} - 100 q^{57} - 397 q^{58} + 16 q^{61} + 101 q^{62} + 367 q^{64} - 1192 q^{66} + 10 q^{68} - 300 q^{69} + 1357 q^{72} + 26 q^{73} + 999 q^{74} - 838 q^{76} + 88 q^{77} + 5 q^{78} + 4950 q^{81} - 498 q^{82} + 730 q^{84} - 94 q^{86} + 391 q^{88} + 36 q^{89} - 572 q^{92} + 30 q^{93} - 888 q^{94} - 432 q^{96} - 364 q^{97} - 862 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3100, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(124, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(620, [\chi])\)\(^{\oplus 2}\)