Properties

Label 1900.3.bv
Level $1900$
Weight $3$
Character orbit 1900.bv
Rep. character $\chi_{1900}(141,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $800$
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.bv (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(900\)

Dimensions

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

Total New Old
Modular forms 4848 800 4048
Cusp forms 4752 800 3952
Eisenstein series 96 0 96

Trace form

\( 800 q + q^{5} + 12 q^{7} - 300 q^{9} + O(q^{10}) \) \( 800 q + q^{5} + 12 q^{7} - 300 q^{9} + 30 q^{11} + 87 q^{15} - 39 q^{17} + 30 q^{19} + 66 q^{23} - 37 q^{25} - 90 q^{29} - 18 q^{33} - 7 q^{35} + 240 q^{39} + 230 q^{43} + 400 q^{45} + 40 q^{47} + 5500 q^{49} - 150 q^{51} + 18 q^{53} + 215 q^{55} - 606 q^{57} + 360 q^{59} - 90 q^{61} - 423 q^{63} + 264 q^{67} - 885 q^{71} + 356 q^{73} - 156 q^{77} - 180 q^{79} + 740 q^{81} - 214 q^{83} - 4 q^{85} - 178 q^{87} - 90 q^{89} + 80 q^{93} + 475 q^{95} - 393 q^{97} - 70 q^{99} + O(q^{100}) \)

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

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