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Properties

Label 1900.2.bt
Level $1900$
Weight $2$
Character orbit 1900.bt
Rep. character $\chi_{1900}(429,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $400$
Sturm bound $600$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.bt (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).

Total New Old
Modular forms 2448 400 2048
Cusp forms 2352 400 1952
Eisenstein series 96 0 96

Trace form

\( 400 q - q^{5} - 50 q^{9} + O(q^{10}) \) \( 400 q - q^{5} - 50 q^{9} + 6 q^{11} - 15 q^{15} + 5 q^{17} + 6 q^{19} + 4 q^{21} + q^{25} - 30 q^{27} + 6 q^{29} - 10 q^{33} + 7 q^{35} - 24 q^{39} - 16 q^{41} - 168 q^{45} - 30 q^{47} - 380 q^{49} + 22 q^{51} - 20 q^{53} - 13 q^{55} + 12 q^{59} + 14 q^{61} - 65 q^{63} - 82 q^{65} + 40 q^{67} - 40 q^{69} - 11 q^{71} + 80 q^{73} + 34 q^{75} + 40 q^{77} + 4 q^{79} + 58 q^{81} - 10 q^{83} - 6 q^{85} + 230 q^{87} + 30 q^{89} - 8 q^{91} + 13 q^{95} + 15 q^{97} + 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

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