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Properties

Label 1450.2.o
Level $1450$
Weight $2$
Character orbit 1450.o
Rep. character $\chi_{1450}(231,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $296$
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.o (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 725 \)
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 920 296 624
Cusp forms 888 296 592
Eisenstein series 32 0 32

Trace form

\( 296 q + 74 q^{4} - 4 q^{6} + 8 q^{7} + 70 q^{9} + O(q^{10}) \) \( 296 q + 74 q^{4} - 4 q^{6} + 8 q^{7} + 70 q^{9} + 8 q^{13} - 74 q^{16} - 8 q^{22} - 24 q^{23} - 16 q^{24} - 32 q^{25} + 12 q^{28} + 8 q^{29} - 6 q^{30} + 44 q^{33} - 8 q^{34} - 70 q^{36} + 28 q^{38} - 12 q^{42} + 16 q^{45} + 256 q^{49} - 8 q^{51} - 8 q^{52} + 4 q^{54} + 96 q^{57} - 20 q^{58} - 12 q^{59} - 8 q^{63} + 74 q^{64} - 114 q^{65} + 64 q^{67} + 36 q^{71} - 72 q^{74} - 42 q^{78} - 122 q^{81} - 32 q^{82} - 56 q^{83} - 20 q^{86} - 4 q^{87} - 12 q^{88} + 88 q^{91} - 16 q^{92} + 44 q^{93} + 16 q^{94} - 4 q^{96} + O(q^{100}) \)

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

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