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Properties

Label 1900.3.bo
Level $1900$
Weight $3$
Character orbit 1900.bo
Rep. character $\chi_{1900}(251,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $2244$
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.bo (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(900\)

Dimensions

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

Total New Old
Modular forms 3672 2316 1356
Cusp forms 3528 2244 1284
Eisenstein series 144 72 72

Trace form

\( 2244 q + 6 q^{2} - 36 q^{6} + 3 q^{8} + 24 q^{9} + O(q^{10}) \) \( 2244 q + 6 q^{2} - 36 q^{6} + 3 q^{8} + 24 q^{9} + 3 q^{12} - 12 q^{13} + 15 q^{14} + 24 q^{16} + 12 q^{17} + 12 q^{18} + 90 q^{21} + 18 q^{22} - 180 q^{24} - 81 q^{26} + 216 q^{28} + 12 q^{29} - 39 q^{32} + 126 q^{33} - 60 q^{34} + 21 q^{36} + 24 q^{37} - 30 q^{38} - 240 q^{41} + 381 q^{42} + 165 q^{44} + 126 q^{46} - 363 q^{48} + 7104 q^{49} + 261 q^{52} - 12 q^{53} + 579 q^{54} + 258 q^{56} + 12 q^{57} + 84 q^{58} - 300 q^{61} - 312 q^{62} - 315 q^{64} + 420 q^{66} + 240 q^{68} + 294 q^{69} - 414 q^{72} + 300 q^{73} - 303 q^{74} - 90 q^{76} + 468 q^{77} - 237 q^{78} - 186 q^{81} + 771 q^{82} - 555 q^{84} - 492 q^{86} + 75 q^{88} - 300 q^{89} + 1104 q^{92} + 498 q^{93} - 162 q^{94} + 882 q^{96} + 120 q^{97} - 1377 q^{98} + O(q^{100}) \)

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

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