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Properties

Label 1550.3.cd
Level $1550$
Weight $3$
Character orbit 1550.cd
Rep. character $\chi_{1550}(161,\cdot)$
Character field $\Q(\zeta_{30})$
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.cd (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 1280 q - 640 q^{4} - 24 q^{5} + 8 q^{7} - 520 q^{9} + O(q^{10}) \) \( 1280 q - 640 q^{4} - 24 q^{5} + 8 q^{7} - 520 q^{9} + 16 q^{10} - 1280 q^{16} + 12 q^{20} + 24 q^{22} - 72 q^{25} - 24 q^{28} + 224 q^{33} + 180 q^{35} - 1040 q^{36} - 144 q^{37} - 208 q^{38} + 32 q^{40} + 90 q^{41} + 504 q^{42} - 792 q^{43} - 296 q^{45} + 60 q^{47} - 4440 q^{49} + 48 q^{50} + 220 q^{51} + 72 q^{53} - 618 q^{55} + 288 q^{57} + 30 q^{59} + 160 q^{62} + 136 q^{63} - 2560 q^{64} - 612 q^{65} + 282 q^{67} + 220 q^{69} - 928 q^{70} - 100 q^{71} - 72 q^{73} - 1500 q^{75} - 768 q^{78} + 24 q^{80} + 1180 q^{81} - 96 q^{82} - 852 q^{83} - 360 q^{86} - 486 q^{87} - 192 q^{88} - 24 q^{90} - 860 q^{93} - 828 q^{95} + 576 q^{97} + 112 q^{98} + 120 q^{99} + O(q^{100}) \)

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

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