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Properties

Label 2850.2.ce
Level $2850$
Weight $2$
Character orbit 2850.ce
Rep. character $\chi_{2850}(61,\cdot)$
Character field $\Q(\zeta_{45})$
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.ce (of order \(45\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{45})\)
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

\( 2400 q - 24 q^{7} + O(q^{10}) \) \( 2400 q - 24 q^{7} + 36 q^{11} + 24 q^{15} + 24 q^{20} + 36 q^{22} + 72 q^{23} - 132 q^{25} + 72 q^{29} + 36 q^{33} + 24 q^{35} - 408 q^{43} - 12 q^{45} - 84 q^{46} + 72 q^{47} - 1224 q^{49} - 72 q^{53} + 180 q^{55} - 24 q^{57} + 72 q^{59} - 12 q^{60} - 144 q^{61} - 48 q^{62} + 300 q^{64} - 48 q^{67} - 24 q^{68} - 48 q^{69} - 24 q^{70} - 24 q^{71} - 72 q^{73} + 96 q^{77} - 48 q^{78} + 96 q^{79} + 96 q^{82} + 108 q^{83} - 24 q^{84} + 144 q^{85} - 36 q^{87} + 144 q^{89} + 96 q^{92} + 192 q^{94} - 12 q^{95} - 264 q^{97} - 288 q^{98} + O(q^{100}) \)

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

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