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Properties

Label 1900.2.z
Level $1900$
Weight $2$
Character orbit 1900.z
Rep. character $\chi_{1900}(229,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $184$
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.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(600\)

Dimensions

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

Total New Old
Modular forms 1224 184 1040
Cusp forms 1176 184 992
Eisenstein series 48 0 48

Trace form

\( 184 q - 9 q^{5} + 46 q^{9} + O(q^{10}) \) \( 184 q - 9 q^{5} + 46 q^{9} - 7 q^{11} + 10 q^{15} + 5 q^{17} + 2 q^{19} + 10 q^{23} + 15 q^{25} + 30 q^{27} - 8 q^{29} + 24 q^{31} - 50 q^{33} + 18 q^{35} + 20 q^{37} - 20 q^{39} - 10 q^{41} + 7 q^{45} - 218 q^{49} - 24 q^{51} - 40 q^{53} - 21 q^{55} + 6 q^{59} - 10 q^{61} + 25 q^{63} + 12 q^{65} - 30 q^{67} + 20 q^{69} - 20 q^{71} + 40 q^{73} - 24 q^{75} + 56 q^{79} - 100 q^{81} + 60 q^{83} + 10 q^{85} + 62 q^{89} - 56 q^{91} - q^{95} - 20 q^{97} + 2 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)