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Properties

Label 1900.3.r
Level $1900$
Weight $3$
Character orbit 1900.r
Rep. character $\chi_{1900}(1151,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $748$
Sturm bound $900$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(900\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1900, [\chi])\).

Total New Old
Modular forms 1224 772 452
Cusp forms 1176 748 428
Eisenstein series 48 24 24

Trace form

\( 748 q + q^{2} + 3 q^{4} + 11 q^{6} - 2 q^{8} + 1084 q^{9} + O(q^{10}) \) \( 748 q + q^{2} + 3 q^{4} + 11 q^{6} - 2 q^{8} + 1084 q^{9} + 22 q^{12} + 10 q^{13} - 2 q^{14} - 17 q^{16} - 22 q^{17} + 28 q^{18} - 48 q^{21} - 33 q^{22} + 19 q^{24} + 68 q^{26} - 18 q^{28} + 2 q^{29} - 49 q^{32} + 4 q^{33} - 42 q^{34} + 106 q^{36} - 72 q^{37} + 56 q^{38} + 62 q^{41} + 36 q^{42} - 89 q^{44} + 100 q^{46} - 229 q^{48} - 4628 q^{49} - 116 q^{52} + 10 q^{53} - 269 q^{54} - 124 q^{56} + 6 q^{57} + 228 q^{58} - 22 q^{61} - 292 q^{62} - 366 q^{64} + 109 q^{66} + 392 q^{68} + 284 q^{69} - 218 q^{72} - 130 q^{73} - 44 q^{74} - 117 q^{76} - 512 q^{77} - 232 q^{78} - 2942 q^{81} - 101 q^{82} + 992 q^{84} - 180 q^{86} - 694 q^{88} + 10 q^{89} - 444 q^{92} - 40 q^{93} + 376 q^{94} + 474 q^{96} - 370 q^{97} - 45 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)