Properties

Label 1450.2.m
Level $1450$
Weight $2$
Character orbit 1450.m
Rep. character $\chi_{1450}(289,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $304$
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.m (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 912 304 608
Cusp forms 880 304 576
Eisenstein series 32 0 32

Trace form

\( 304 q - 76 q^{4} + 2 q^{5} + 4 q^{6} - 80 q^{9} + O(q^{10}) \) \( 304 q - 76 q^{4} + 2 q^{5} + 4 q^{6} - 80 q^{9} - 76 q^{16} - 8 q^{20} - 40 q^{23} - 16 q^{24} + 30 q^{25} + 20 q^{28} + 18 q^{29} + 6 q^{30} + 40 q^{33} - 38 q^{34} - 80 q^{36} + 20 q^{42} - 22 q^{45} - 344 q^{49} + 8 q^{51} + 90 q^{53} + 4 q^{54} - 12 q^{59} - 76 q^{64} - 60 q^{65} + 80 q^{67} - 36 q^{71} - 52 q^{74} - 130 q^{78} + 2 q^{80} - 28 q^{81} + 20 q^{86} + 80 q^{87} + 20 q^{88} - 88 q^{91} + 16 q^{94} + 4 q^{96} + O(q^{100}) \)

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

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