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Properties

Label 1900.2.cf
Level $1900$
Weight $2$
Character orbit 1900.cf
Rep. character $\chi_{1900}(217,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $800$
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.cf (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(600\)

Dimensions

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

Total New Old
Modular forms 4896 800 4096
Cusp forms 4704 800 3904
Eisenstein series 192 0 192

Trace form

\( 800 q + 2 q^{5} + 4 q^{7} + O(q^{10}) \) \( 800 q + 2 q^{5} + 4 q^{7} + 18 q^{15} + 2 q^{17} - 20 q^{19} + 4 q^{23} - 10 q^{25} - 60 q^{29} - 12 q^{33} - 14 q^{35} - 80 q^{39} - 30 q^{43} + 84 q^{45} + 10 q^{47} - 18 q^{53} + 64 q^{55} - 142 q^{57} + 120 q^{59} - 42 q^{63} + 48 q^{67} - 36 q^{73} + 188 q^{77} - 100 q^{81} + 84 q^{83} - 44 q^{85} - 196 q^{87} - 60 q^{93} + 104 q^{95} - 6 q^{97} + O(q^{100}) \)

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

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