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Properties

Label 1900.3.b
Level $1900$
Weight $3$
Character orbit 1900.b
Rep. character $\chi_{1900}(951,\cdot)$
Character field $\Q$
Dimension $342$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Sturm bound: \(900\)

Dimensions

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

Total New Old
Modular forms 612 342 270
Cusp forms 588 342 246
Eisenstein series 24 0 24

Trace form

\( 342 q - 2 q^{2} - 6 q^{4} - 6 q^{6} - 8 q^{8} - 1026 q^{9} + O(q^{10}) \) \( 342 q - 2 q^{2} - 6 q^{4} - 6 q^{6} - 8 q^{8} - 1026 q^{9} + 64 q^{12} - 12 q^{13} + 52 q^{14} - 6 q^{16} - 20 q^{17} + 22 q^{18} + 16 q^{21} - 136 q^{22} - 114 q^{24} - 134 q^{26} - 26 q^{28} - 60 q^{29} + 128 q^{32} + 48 q^{33} + 236 q^{34} - 20 q^{36} + 116 q^{37} - 100 q^{41} - 198 q^{42} + 68 q^{44} + 288 q^{46} - 92 q^{48} - 2474 q^{49} - 24 q^{52} - 332 q^{53} - 6 q^{54} - 292 q^{56} - 366 q^{58} + 100 q^{61} - 132 q^{62} + 246 q^{64} - 88 q^{66} - 454 q^{68} + 96 q^{69} + 92 q^{72} + 268 q^{73} + 656 q^{74} + 344 q^{77} + 12 q^{78} + 2998 q^{81} + 516 q^{82} + 456 q^{84} - 752 q^{86} + 12 q^{88} - 20 q^{89} - 126 q^{92} - 592 q^{93} - 56 q^{94} - 790 q^{96} - 260 q^{97} + 150 q^{98} + O(q^{100}) \)

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

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