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Properties

Label 2800.2.dy
Level $2800$
Weight $2$
Character orbit 2800.dy
Rep. character $\chi_{2800}(97,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $944$
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.dy (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 3936 976 2960
Cusp forms 3744 944 2800
Eisenstein series 192 32 160

Trace form

\( 944 q + 8 q^{7} - 20 q^{9} + O(q^{10}) \) \( 944 q + 8 q^{7} - 20 q^{9} + 12 q^{11} + 16 q^{15} - 6 q^{21} - 8 q^{23} - 16 q^{25} - 20 q^{29} + 20 q^{35} - 16 q^{37} + 20 q^{39} + 16 q^{43} + 32 q^{51} - 16 q^{53} + 12 q^{57} + 64 q^{63} + 40 q^{67} + 12 q^{71} + 6 q^{77} + 20 q^{79} + 192 q^{81} - 16 q^{85} + 6 q^{91} + 36 q^{93} + 116 q^{95} + O(q^{100}) \)

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

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