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Properties

Label 1550.3.bw
Level $1550$
Weight $3$
Character orbit 1550.bw
Rep. character $\chi_{1550}(33,\cdot)$
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.bw (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

\( 1280 q + 8 q^{3} + 16 q^{7} + O(q^{10}) \) \( 1280 q + 8 q^{3} + 16 q^{7} + 32 q^{10} - 24 q^{12} - 16 q^{15} + 1280 q^{16} + 72 q^{20} - 32 q^{22} - 56 q^{23} - 120 q^{25} + 92 q^{27} - 32 q^{28} - 240 q^{30} + 40 q^{33} - 168 q^{35} - 1920 q^{36} + 288 q^{37} + 240 q^{38} - 96 q^{42} + 312 q^{43} - 364 q^{45} + 396 q^{47} + 48 q^{48} + 200 q^{49} - 96 q^{50} + 224 q^{53} - 1200 q^{54} + 328 q^{55} - 228 q^{57} - 128 q^{58} + 400 q^{59} - 168 q^{60} + 104 q^{62} + 248 q^{63} - 240 q^{65} - 168 q^{67} + 1100 q^{69} - 608 q^{70} - 360 q^{71} + 120 q^{73} + 408 q^{75} + 1280 q^{77} - 496 q^{78} - 200 q^{79} + 2320 q^{81} - 768 q^{82} + 196 q^{83} + 104 q^{85} - 928 q^{87} + 64 q^{88} - 300 q^{89} - 224 q^{90} - 112 q^{92} - 2532 q^{93} - 144 q^{95} - 812 q^{97} - 96 q^{98} + O(q^{100}) \)

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

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