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Properties

Label 1450.2.k
Level $1450$
Weight $2$
Character orbit 1450.k
Rep. character $\chi_{1450}(291,\cdot)$
Character field $\Q(\zeta_{5})$
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.k (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(450\)

Dimensions

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

Total New Old
Modular forms 912 280 632
Cusp forms 880 280 600
Eisenstein series 32 0 32

Trace form

\( 280 q + 8 q^{3} - 70 q^{4} - 12 q^{5} + 8 q^{7} - 62 q^{9} + O(q^{10}) \) \( 280 q + 8 q^{3} - 70 q^{4} - 12 q^{5} + 8 q^{7} - 62 q^{9} - 8 q^{11} - 12 q^{12} + 8 q^{14} - 24 q^{15} - 70 q^{16} - 12 q^{17} + 16 q^{18} + 4 q^{19} + 8 q^{20} + 8 q^{21} - 24 q^{22} + 12 q^{23} - 36 q^{25} - 48 q^{26} - 4 q^{27} + 8 q^{28} + 6 q^{29} - 6 q^{30} + 24 q^{31} - 40 q^{33} + 20 q^{35} - 62 q^{36} + 40 q^{37} + 12 q^{38} + 16 q^{39} + 16 q^{41} + 56 q^{42} + 40 q^{43} + 12 q^{44} - 28 q^{45} - 16 q^{46} - 8 q^{47} - 12 q^{48} + 320 q^{49} + 32 q^{50} + 24 q^{51} + 72 q^{53} + 12 q^{54} - 44 q^{55} + 8 q^{56} - 96 q^{57} + 12 q^{59} - 4 q^{60} + 20 q^{61} - 56 q^{62} - 88 q^{63} - 70 q^{64} + 82 q^{65} + 48 q^{66} + 28 q^{67} + 8 q^{68} - 120 q^{69} - 28 q^{70} + 48 q^{71} + 16 q^{72} + 16 q^{73} - 56 q^{75} - 16 q^{76} + 24 q^{77} + 30 q^{78} + 8 q^{80} - 90 q^{81} - 112 q^{82} - 108 q^{83} + 8 q^{84} - 16 q^{85} + 24 q^{86} + 16 q^{88} + 28 q^{89} - 128 q^{90} + 32 q^{91} - 28 q^{92} + 28 q^{93} + 32 q^{94} + 72 q^{95} + 12 q^{97} + 48 q^{98} + 32 q^{99} + O(q^{100}) \)

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

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