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Properties

Label 1550.2.cx
Level $1550$
Weight $2$
Character orbit 1550.cx
Rep. character $\chi_{1550}(37,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1280$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1550 = 2 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1550.cx (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1550, [\chi])\).

Total New Old
Modular forms 3904 1280 2624
Cusp forms 3776 1280 2496
Eisenstein series 128 0 128

Trace form

\( 1280 q - 4 q^{7} + O(q^{10}) \) \( 1280 q - 4 q^{7} - 8 q^{10} + 320 q^{16} + 4 q^{20} + 108 q^{22} - 40 q^{25} - 16 q^{28} + 16 q^{33} + 48 q^{35} - 160 q^{36} + 72 q^{37} + 8 q^{38} + 48 q^{42} + 72 q^{43} - 28 q^{45} + 40 q^{47} - 8 q^{50} - 12 q^{53} - 120 q^{55} - 24 q^{57} + 60 q^{59} - 40 q^{62} + 24 q^{63} + 312 q^{65} + 4 q^{67} - 140 q^{69} - 40 q^{70} + 40 q^{71} + 192 q^{73} - 12 q^{75} + 208 q^{78} - 240 q^{79} - 80 q^{81} + 8 q^{82} - 348 q^{83} - 92 q^{87} + 12 q^{88} + 28 q^{90} + 40 q^{93} + 104 q^{95} - 128 q^{97} + 8 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1550, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1550, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1550, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 2}\)