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Properties

Label 2800.2.bp
Level $2800$
Weight $2$
Character orbit 2800.bp
Rep. character $\chi_{2800}(561,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $360$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2800.bp (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2800, [\chi])\).

Total New Old
Modular forms 1968 360 1608
Cusp forms 1872 360 1512
Eisenstein series 96 0 96

Trace form

\( 360 q + 2 q^{5} - 90 q^{9} + O(q^{10}) \) \( 360 q + 2 q^{5} - 90 q^{9} - 12 q^{11} + 4 q^{13} - 12 q^{15} - 4 q^{17} - 2 q^{25} - 24 q^{27} + 4 q^{29} - 30 q^{37} + 16 q^{39} - 4 q^{41} + 32 q^{43} + 10 q^{45} - 24 q^{47} + 360 q^{49} + 96 q^{51} - 6 q^{53} - 8 q^{55} + 16 q^{57} + 20 q^{61} + 46 q^{65} - 48 q^{67} + 28 q^{71} - 20 q^{73} + 32 q^{75} + 20 q^{79} - 114 q^{81} + 40 q^{83} - 30 q^{85} + 128 q^{87} + 30 q^{89} - 12 q^{91} - 64 q^{93} - 32 q^{95} - 4 q^{97} + 144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)