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Properties

Label 1450.2.y
Level $1450$
Weight $2$
Character orbit 1450.y
Rep. character $\chi_{1450}(43,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $540$
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.y (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 145 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(450\)

Dimensions

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

Total New Old
Modular forms 2844 540 2304
Cusp forms 2556 540 2016
Eisenstein series 288 0 288

Trace form

\( 540 q + 90 q^{4} - 74 q^{9} + O(q^{10}) \) \( 540 q + 90 q^{4} - 74 q^{9} + 16 q^{11} - 38 q^{13} + 8 q^{14} - 90 q^{16} + 80 q^{21} - 60 q^{26} + 60 q^{27} + 80 q^{31} + 4 q^{33} - 32 q^{34} + 130 q^{36} - 72 q^{37} - 28 q^{38} - 48 q^{39} - 34 q^{41} - 8 q^{42} + 40 q^{43} + 96 q^{44} + 8 q^{46} + 64 q^{47} - 168 q^{49} - 18 q^{52} + 52 q^{53} - 8 q^{56} - 48 q^{57} - 2 q^{58} - 14 q^{61} + 136 q^{63} + 90 q^{64} + 48 q^{66} + 16 q^{67} + 208 q^{69} + 28 q^{73} - 224 q^{74} + 84 q^{77} + 152 q^{78} + 32 q^{79} - 58 q^{81} + 34 q^{82} + 56 q^{83} + 32 q^{84} - 76 q^{87} - 30 q^{89} - 52 q^{93} + 168 q^{94} - 8 q^{97} - 114 q^{98} - 64 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 2}\)