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Properties

Label 1450.2.n
Level $1450$
Weight $2$
Character orbit 1450.n
Rep. character $\chi_{1450}(59,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $280$
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.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(450\)

Dimensions

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

Total New Old
Modular forms 920 280 640
Cusp forms 888 280 608
Eisenstein series 32 0 32

Trace form

\( 280 q + 70 q^{4} + 20 q^{5} + 78 q^{9} + O(q^{10}) \) \( 280 q + 70 q^{4} + 20 q^{5} + 78 q^{9} + 8 q^{11} + 20 q^{12} + 8 q^{14} + 32 q^{15} - 70 q^{16} - 20 q^{17} + 4 q^{19} - 8 q^{21} - 40 q^{22} + 20 q^{23} - 36 q^{25} + 48 q^{26} - 60 q^{27} + 6 q^{29} - 34 q^{30} - 24 q^{31} + 100 q^{33} - 28 q^{35} - 78 q^{36} + 16 q^{39} - 16 q^{41} + 12 q^{44} - 76 q^{45} + 16 q^{46} - 40 q^{47} + 20 q^{48} - 240 q^{49} + 16 q^{50} - 24 q^{51} + 12 q^{54} + 4 q^{55} - 8 q^{56} + 12 q^{59} - 12 q^{60} - 20 q^{61} - 40 q^{63} + 70 q^{64} - 10 q^{65} - 48 q^{66} + 60 q^{67} - 60 q^{70} + 32 q^{71} + 80 q^{73} + 120 q^{75} + 16 q^{76} + 80 q^{77} + 30 q^{78} + 30 q^{81} - 100 q^{83} + 8 q^{84} + 72 q^{85} - 24 q^{86} - 52 q^{89} + 64 q^{90} - 32 q^{91} + 20 q^{92} + 32 q^{94} + 8 q^{95} + 60 q^{97} - 48 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 2}\)