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Properties

Label 2800.2.fz
Level $2800$
Weight $2$
Character orbit 2800.fz
Rep. character $\chi_{2800}(17,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1888$
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.fz (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 7872 1952 5920
Cusp forms 7488 1888 5600
Eisenstein series 384 64 320

Trace form

\( 1888 q + 24 q^{3} - 24 q^{5} + 16 q^{7} - 10 q^{9} + O(q^{10}) \) \( 1888 q + 24 q^{3} - 24 q^{5} + 16 q^{7} - 10 q^{9} + 6 q^{11} + 32 q^{15} - 24 q^{17} + 30 q^{19} - 12 q^{21} - 4 q^{23} - 8 q^{25} - 40 q^{29} + 18 q^{31} + 4 q^{35} - 8 q^{37} + 10 q^{39} + 32 q^{43} - 24 q^{45} + 60 q^{47} + 16 q^{51} - 8 q^{53} - 12 q^{57} + 30 q^{59} - 18 q^{61} - 40 q^{63} - 24 q^{65} + 20 q^{67} + 24 q^{71} - 24 q^{73} + 24 q^{75} - 30 q^{77} + 10 q^{79} - 210 q^{81} - 32 q^{85} + 42 q^{87} - 30 q^{89} + 12 q^{91} - 60 q^{93} - 56 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1400, [\chi])\)\(^{\oplus 2}\)