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Properties

Label 3100.3.ci
Level $3100$
Weight $3$
Character orbit 3100.ci
Rep. character $\chi_{3100}(1151,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $2408$
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.ci (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 124 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 3888 2456 1432
Cusp forms 3792 2408 1384
Eisenstein series 96 48 48

Trace form

\( 2408 q + 3 q^{2} - q^{4} - 34 q^{6} + 27 q^{8} + 1776 q^{9} + O(q^{10}) \) \( 2408 q + 3 q^{2} - q^{4} - 34 q^{6} + 27 q^{8} + 1776 q^{9} - 24 q^{12} - 10 q^{13} + 2 q^{14} + 43 q^{16} + 6 q^{17} + 10 q^{18} - 54 q^{21} + 56 q^{22} - 87 q^{24} - 92 q^{26} + 8 q^{28} + 6 q^{29} + 98 q^{32} + 90 q^{33} - 79 q^{34} - 28 q^{36} - 64 q^{37} - 58 q^{38} - 18 q^{41} - 202 q^{42} - 138 q^{44} + 219 q^{46} + 14 q^{48} + 4136 q^{49} - 227 q^{52} - 154 q^{53} - 332 q^{54} + 428 q^{56} - 92 q^{57} + 193 q^{58} + 176 q^{61} + 130 q^{62} + 467 q^{64} - 122 q^{66} + 482 q^{68} + 474 q^{69} + 668 q^{72} + 358 q^{73} + 333 q^{74} - 365 q^{76} + 218 q^{77} + 487 q^{78} - 4968 q^{81} + 186 q^{82} - 445 q^{84} + 505 q^{86} - 232 q^{88} - 18 q^{89} + 182 q^{92} - 150 q^{93} - 90 q^{94} - 294 q^{96} + 382 q^{97} + 244 q^{98} + O(q^{100}) \)

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

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