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Properties

Label 1550.3.da
Level $1550$
Weight $3$
Character orbit 1550.da
Rep. character $\chi_{1550}(173,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2560$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1550 = 2 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1550.da (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1550, [\chi])\).

Total New Old
Modular forms 7744 2560 5184
Cusp forms 7616 2560 5056
Eisenstein series 128 0 128

Trace form

\( 2560 q + 12 q^{3} + 8 q^{7} + 100 q^{9} + O(q^{10}) \) \( 2560 q + 12 q^{3} + 8 q^{7} + 100 q^{9} + 48 q^{10} - 16 q^{12} + 112 q^{15} + 2560 q^{16} + 216 q^{20} - 16 q^{22} - 124 q^{23} + 20 q^{25} + 480 q^{27} - 16 q^{28} + 400 q^{29} + 288 q^{30} - 456 q^{33} - 192 q^{35} + 1920 q^{36} + 536 q^{37} - 80 q^{38} + 192 q^{42} - 384 q^{43} + 48 q^{45} - 156 q^{47} + 32 q^{48} + 32 q^{50} + 48 q^{53} + 680 q^{55} - 1144 q^{57} + 128 q^{58} + 200 q^{59} + 168 q^{60} - 464 q^{62} + 232 q^{63} + 2348 q^{65} + 1356 q^{67} + 176 q^{70} + 120 q^{71} + 208 q^{73} + 2924 q^{75} + 840 q^{77} - 512 q^{78} + 1800 q^{79} - 3020 q^{81} + 96 q^{82} + 1368 q^{83} - 104 q^{85} - 988 q^{87} - 608 q^{88} - 112 q^{90} + 192 q^{92} + 416 q^{93} - 1192 q^{95} - 40 q^{97} - 112 q^{98} + 5400 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1550, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1550, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1550, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 2}\)