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Properties

Label 1650.2.cc
Level $1650$
Weight $2$
Character orbit 1650.cc
Rep. character $\chi_{1650}(379,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $240$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1650.cc (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1650, [\chi])\).

Total New Old
Modular forms 1472 240 1232
Cusp forms 1408 240 1168
Eisenstein series 64 0 64

Trace form

\( 240 q - 240 q^{4} + 8 q^{5} - 4 q^{6} + 30 q^{7} + 60 q^{9} + O(q^{10}) \) \( 240 q - 240 q^{4} + 8 q^{5} - 4 q^{6} + 30 q^{7} + 60 q^{9} - 6 q^{10} - 8 q^{11} - 4 q^{15} + 240 q^{16} - 20 q^{17} - 16 q^{19} - 8 q^{20} - 8 q^{21} + 10 q^{22} + 4 q^{24} + 34 q^{25} - 30 q^{28} + 8 q^{30} + 2 q^{31} - 36 q^{35} - 60 q^{36} + 40 q^{37} + 6 q^{40} - 48 q^{41} + 10 q^{42} + 8 q^{44} + 12 q^{45} - 12 q^{46} - 20 q^{47} + 54 q^{49} + 16 q^{50} - 8 q^{51} + 4 q^{54} - 62 q^{55} - 20 q^{57} + 48 q^{59} + 4 q^{60} - 12 q^{61} - 60 q^{62} + 10 q^{63} - 240 q^{64} + 116 q^{65} + 20 q^{67} + 20 q^{68} + 16 q^{69} + 10 q^{70} - 16 q^{71} + 60 q^{73} - 56 q^{75} + 16 q^{76} + 20 q^{77} - 2 q^{79} + 8 q^{80} - 60 q^{81} + 40 q^{82} + 140 q^{83} + 8 q^{84} - 40 q^{85} - 48 q^{86} - 10 q^{88} - 4 q^{90} - 4 q^{91} + 32 q^{94} + 80 q^{95} - 4 q^{96} + 10 q^{97} - 80 q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1650, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)