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Properties

Label 1450.2.be
Level $1450$
Weight $2$
Character orbit 1450.be
Rep. character $\chi_{1450}(81,\cdot)$
Character field $\Q(\zeta_{35})$
Dimension $1824$
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.be (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 725 \)
Character field: \(\Q(\zeta_{35})\)
Sturm bound: \(450\)

Dimensions

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

Total New Old
Modular forms 5472 1824 3648
Cusp forms 5280 1824 3456
Eisenstein series 192 0 192

Trace form

\( 1824 q + 2 q^{2} + 76 q^{4} + 2 q^{5} + 4 q^{6} + 8 q^{7} + 2 q^{8} + 80 q^{9} + O(q^{10}) \) \( 1824 q + 2 q^{2} + 76 q^{4} + 2 q^{5} + 4 q^{6} + 8 q^{7} + 2 q^{8} + 80 q^{9} + 10 q^{10} - 28 q^{13} + 10 q^{15} + 76 q^{16} + 28 q^{17} - 40 q^{18} - 24 q^{19} + 20 q^{20} + 24 q^{21} + 8 q^{22} - 24 q^{23} - 16 q^{24} - 56 q^{25} - 30 q^{26} + 90 q^{27} - 12 q^{28} - 6 q^{29} - 36 q^{30} - 12 q^{31} - 8 q^{32} - 4 q^{33} + 83 q^{34} - 16 q^{35} + 80 q^{36} - 78 q^{37} + 28 q^{38} - 11 q^{40} - 24 q^{41} - 12 q^{42} - 88 q^{43} - 17 q^{45} - 36 q^{47} - 328 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} + 51 q^{53} + 28 q^{54} + 8 q^{55} + 96 q^{57} + 30 q^{58} - 96 q^{59} + 60 q^{60} + 140 q^{61} - 56 q^{63} + 76 q^{64} - 87 q^{65} - 32 q^{67} - 92 q^{68} + 16 q^{69} - 80 q^{70} + 90 q^{71} + 10 q^{72} - 70 q^{73} - 52 q^{74} - 184 q^{75} - 40 q^{76} - 156 q^{77} + 132 q^{78} + 2 q^{80} - 68 q^{81} + 36 q^{82} + 56 q^{83} + 90 q^{84} - 194 q^{85} - 120 q^{86} - 12 q^{88} - 18 q^{89} + 8 q^{90} + 212 q^{91} + 16 q^{92} + 108 q^{93} + 16 q^{94} - 176 q^{95} + 4 q^{96} - 22 q^{97} + 154 q^{98} + 104 q^{99} + O(q^{100}) \)

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

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