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Properties

Label 3100.3.b
Level $3100$
Weight $3$
Character orbit 3100.b
Rep. character $\chi_{3100}(1551,\cdot)$
Character field $\Q$
Dimension $570$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 972 570 402
Cusp forms 948 570 378
Eisenstein series 24 0 24

Trace form

\( 570 q - 2 q^{2} - 6 q^{4} + 7 q^{8} - 1702 q^{9} + O(q^{10}) \) \( 570 q - 2 q^{2} - 6 q^{4} + 7 q^{8} - 1702 q^{9} + 34 q^{12} - 12 q^{13} + 59 q^{14} - 30 q^{16} - 44 q^{17} - 6 q^{18} + 16 q^{21} - 136 q^{22} - 192 q^{24} - 58 q^{26} - 83 q^{28} - 60 q^{29} + 118 q^{32} + 80 q^{33} + 164 q^{34} + 222 q^{36} + 116 q^{37} + 223 q^{38} - 236 q^{41} - 158 q^{42} - 92 q^{44} + 182 q^{46} - 204 q^{48} - 3942 q^{49} - 16 q^{52} - 188 q^{53} - 176 q^{54} - 112 q^{56} + 112 q^{57} - 140 q^{58} + 100 q^{61} + 291 q^{64} + 92 q^{66} - 254 q^{68} - 112 q^{69} - 77 q^{72} + 180 q^{73} + 142 q^{74} - 35 q^{76} + 272 q^{77} - 252 q^{78} + 4538 q^{81} + 381 q^{82} - 228 q^{84} - 474 q^{86} + 562 q^{88} + 164 q^{89} + 248 q^{92} - 164 q^{94} + 90 q^{96} - 60 q^{97} + 255 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3100, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(124, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(620, [\chi])\)\(^{\oplus 2}\)