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Properties

Label 1450.2.bf
Level $1450$
Weight $2$
Character orbit 1450.bf
Rep. character $\chi_{1450}(71,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $1776$
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.bf (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 725 \)
Character field: \(\Q(\zeta_{70})\)
Sturm bound: \(450\)

Dimensions

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

Total New Old
Modular forms 5520 1776 3744
Cusp forms 5328 1776 3552
Eisenstein series 192 0 192

Trace form

\( 1776 q - 74 q^{4} + 4 q^{6} - 8 q^{7} - 70 q^{9} + O(q^{10}) \) \( 1776 q - 74 q^{4} + 4 q^{6} - 8 q^{7} - 70 q^{9} + 48 q^{13} + 14 q^{15} + 74 q^{16} + 8 q^{22} + 24 q^{23} + 16 q^{24} + 18 q^{25} - 28 q^{26} - 126 q^{27} - 12 q^{28} - 8 q^{29} - 36 q^{30} - 44 q^{33} + 8 q^{34} + 70 q^{36} + 84 q^{37} - 28 q^{38} + 14 q^{40} + 12 q^{42} + 56 q^{43} - 16 q^{45} - 256 q^{49} + 28 q^{50} + 8 q^{51} + 8 q^{52} + 84 q^{53} - 4 q^{54} - 56 q^{55} - 96 q^{57} + 20 q^{58} + 96 q^{59} - 56 q^{60} - 168 q^{61} - 104 q^{63} - 74 q^{64} + 86 q^{65} - 64 q^{67} + 90 q^{71} - 28 q^{73} + 72 q^{74} - 56 q^{76} + 84 q^{77} - 168 q^{78} - 102 q^{81} + 32 q^{82} + 56 q^{83} - 126 q^{84} - 28 q^{85} - 120 q^{86} + 4 q^{87} + 12 q^{88} - 70 q^{90} + 164 q^{91} + 16 q^{92} - 44 q^{93} - 16 q^{94} + 4 q^{96} + 112 q^{97} - 168 q^{98} + O(q^{100}) \)

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

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