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Properties

Label 1900.3.bf
Level $1900$
Weight $3$
Character orbit 1900.bf
Rep. character $\chi_{1900}(657,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $240$
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.bf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(900\)

Dimensions

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

Total New Old
Modular forms 2472 240 2232
Cusp forms 2328 240 2088
Eisenstein series 144 0 144

Trace form

\( 240 q + 12 q^{7} + O(q^{10}) \) \( 240 q + 12 q^{7} + 32 q^{11} + 8 q^{13} + 32 q^{17} + 12 q^{21} + 60 q^{23} + 84 q^{27} + 56 q^{31} - 12 q^{33} + 128 q^{37} + 80 q^{41} - 58 q^{43} - 70 q^{47} + 136 q^{51} + 82 q^{53} - 322 q^{57} + 52 q^{61} + 86 q^{63} + 72 q^{67} + 64 q^{71} + 292 q^{73} - 420 q^{77} + 1128 q^{81} + 100 q^{83} - 200 q^{87} + 76 q^{91} - 16 q^{93} + 122 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)