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Properties

Label 2850.2.bh
Level $2850$
Weight $2$
Character orbit 2850.bh
Rep. character $\chi_{2850}(121,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $800$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2850.bh (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2850, [\chi])\).

Total New Old
Modular forms 4864 800 4064
Cusp forms 4736 800 3936
Eisenstein series 128 0 128

Trace form

\( 800 q + 100 q^{4} - 4 q^{5} + 16 q^{7} + 100 q^{9} + O(q^{10}) \) \( 800 q + 100 q^{4} - 4 q^{5} + 16 q^{7} + 100 q^{9} - 24 q^{11} - 16 q^{13} + 4 q^{15} + 100 q^{16} + 12 q^{17} + 12 q^{19} + 8 q^{20} - 8 q^{21} - 12 q^{22} - 12 q^{23} - 8 q^{25} - 8 q^{28} - 24 q^{29} + 32 q^{30} - 12 q^{33} - 16 q^{34} + 28 q^{35} + 100 q^{36} - 16 q^{37} - 16 q^{38} - 96 q^{43} - 8 q^{44} + 8 q^{45} - 16 q^{46} - 32 q^{47} + 816 q^{49} - 32 q^{50} + 32 q^{51} - 16 q^{52} + 72 q^{53} + 12 q^{55} - 72 q^{59} + 4 q^{60} - 32 q^{61} + 16 q^{62} + 12 q^{63} - 200 q^{64} - 72 q^{65} + 88 q^{67} + 16 q^{68} + 16 q^{69} + 20 q^{70} + 8 q^{71} + 64 q^{73} - 16 q^{75} - 8 q^{76} + 128 q^{77} + 16 q^{78} + 16 q^{79} - 4 q^{80} + 100 q^{81} + 16 q^{82} + 112 q^{83} + 16 q^{84} - 20 q^{85} - 48 q^{87} - 16 q^{88} + 24 q^{89} - 16 q^{91} + 8 q^{92} + 64 q^{93} + 32 q^{94} + 108 q^{95} - 20 q^{97} - 80 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2850, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)