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Properties

Label 2850.2.cp
Level $2850$
Weight $2$
Character orbit 2850.cp
Rep. character $\chi_{2850}(139,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $2400$
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.cp (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 14592 2400 12192
Cusp forms 14208 2400 11808
Eisenstein series 384 0 384

Trace form

\( 2400 q + O(q^{10}) \) \( 2400 q - 36 q^{11} - 24 q^{15} - 24 q^{20} + 60 q^{22} + 120 q^{23} + 108 q^{25} + 72 q^{29} + 60 q^{33} - 24 q^{35} + 12 q^{45} + 84 q^{46} + 120 q^{47} + 1176 q^{49} - 108 q^{55} + 72 q^{59} - 12 q^{60} + 144 q^{61} - 300 q^{64} - 48 q^{69} + 72 q^{70} + 24 q^{71} + 96 q^{79} + 60 q^{83} - 24 q^{84} + 240 q^{85} - 60 q^{87} + 144 q^{89} + 192 q^{94} + 60 q^{95} + 360 q^{97} + 480 q^{98} + O(q^{100}) \)

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

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