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Properties

Label 2800.2.q
Level $2800$
Weight $2$
Character orbit 2800.q
Rep. character $\chi_{2800}(401,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $146$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1032 158 874
Cusp forms 888 146 742
Eisenstein series 144 12 132

Trace form

\( 146 q + q^{3} - 66 q^{9} + O(q^{10}) \) \( 146 q + q^{3} - 66 q^{9} + q^{11} + 4 q^{13} + q^{17} - 9 q^{19} - 5 q^{21} + 3 q^{23} - 14 q^{27} + 4 q^{29} + q^{31} - 9 q^{33} + 5 q^{37} - 6 q^{39} - 4 q^{41} + 16 q^{43} - 17 q^{47} + 2 q^{49} + 7 q^{51} + 9 q^{53} - 10 q^{57} - 27 q^{59} + q^{61} + 18 q^{63} - 19 q^{67} - 10 q^{69} + 56 q^{71} + 5 q^{73} + 7 q^{77} - 37 q^{79} - 37 q^{81} - 72 q^{83} - 34 q^{87} + 13 q^{89} - 56 q^{91} + 11 q^{93} - 20 q^{97} + 76 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)