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Properties

Label 1900.3.bb
Level $1900$
Weight $3$
Character orbit 1900.bb
Rep. character $\chi_{1900}(341,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $400$
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.bb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(900\)

Dimensions

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

Total New Old
Modular forms 2424 400 2024
Cusp forms 2376 400 1976
Eisenstein series 48 0 48

Trace form

\( 400 q - q^{5} + 6 q^{7} + 300 q^{9} + O(q^{10}) \) \( 400 q - q^{5} + 6 q^{7} + 300 q^{9} + 15 q^{11} - 15 q^{17} - 30 q^{19} + 60 q^{23} - 101 q^{25} + 70 q^{35} - 240 q^{39} + 214 q^{43} + 599 q^{45} - 112 q^{47} + 2750 q^{49} - 167 q^{55} - 432 q^{57} - 90 q^{61} + 567 q^{63} - 194 q^{73} + 30 q^{77} - 500 q^{81} - 470 q^{83} - 314 q^{85} + 370 q^{87} - 992 q^{93} + 161 q^{95} + 310 q^{99} + O(q^{100}) \)

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

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