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Properties

Label 1450.2.s
Level $1450$
Weight $2$
Character orbit 1450.s
Rep. character $\chi_{1450}(133,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $600$
Sturm bound $450$

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Defining parameters

Level: \( N \) \(=\) \( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1450.s (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 725 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(450\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1450, [\chi])\).

Total New Old
Modular forms 1832 600 1232
Cusp forms 1768 600 1168
Eisenstein series 64 0 64

Trace form

\( 600 q + 150 q^{4} - 150 q^{9} + O(q^{10}) \) \( 600 q + 150 q^{4} - 150 q^{9} - 10 q^{10} - 18 q^{13} - 150 q^{16} - 40 q^{19} + 2 q^{25} + 10 q^{26} - 36 q^{27} - 40 q^{29} + 20 q^{31} - 4 q^{33} + 16 q^{35} + 150 q^{36} - 42 q^{37} + 28 q^{38} + 10 q^{40} + 50 q^{41} - 32 q^{42} - 64 q^{43} - 40 q^{45} + 36 q^{47} - 16 q^{50} + 18 q^{52} - 72 q^{53} + 32 q^{55} + 48 q^{57} + 2 q^{58} - 20 q^{60} + 90 q^{61} - 24 q^{63} + 150 q^{64} - 16 q^{65} - 16 q^{67} + 76 q^{70} + 80 q^{73} - 68 q^{75} - 160 q^{77} - 12 q^{78} + 80 q^{79} - 150 q^{81} - 34 q^{82} - 56 q^{83} - 60 q^{84} + 64 q^{85} + 48 q^{87} - 20 q^{89} - 38 q^{90} + 52 q^{93} - 8 q^{95} - 124 q^{97} + 82 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 2}\)