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Properties

Label 1550.3.bt
Level $1550$
Weight $3$
Character orbit 1550.bt
Rep. character $\chi_{1550}(97,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1280$
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.bt (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 3872 1280 2592
Cusp forms 3808 1280 2528
Eisenstein series 64 0 64

Trace form

\( 1280 q + 8 q^{3} + 16 q^{7} + 100 q^{9} + O(q^{10}) \) \( 1280 q + 8 q^{3} + 16 q^{7} + 100 q^{9} + 32 q^{10} - 24 q^{12} - 96 q^{15} - 5120 q^{16} - 48 q^{20} - 32 q^{22} - 56 q^{23} + 40 q^{25} + 92 q^{27} - 32 q^{28} - 80 q^{33} - 108 q^{35} - 1920 q^{36} + 148 q^{37} + 240 q^{38} + 864 q^{42} - 48 q^{43} - 364 q^{45} - 324 q^{47} - 32 q^{48} + 64 q^{50} + 224 q^{53} + 1200 q^{54} + 868 q^{55} - 8 q^{57} + 192 q^{58} - 168 q^{60} + 424 q^{62} - 232 q^{63} - 660 q^{65} + 372 q^{67} + 300 q^{69} + 312 q^{70} - 360 q^{71} + 120 q^{73} - 232 q^{75} - 280 q^{77} - 496 q^{78} - 400 q^{79} + 3020 q^{81} + 192 q^{82} + 676 q^{83} - 96 q^{85} - 8 q^{87} - 256 q^{88} + 300 q^{89} - 624 q^{90} - 192 q^{92} + 1168 q^{93} - 144 q^{95} + 208 q^{97} + 544 q^{98} + O(q^{100}) \)

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

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