Properties

Label 1400.2.dr
Level $1400$
Weight $2$
Character orbit 1400.dr
Rep. character $\chi_{1400}(17,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $960$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.dr (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1400, [\chi])\).

Total New Old
Modular forms 3968 960 3008
Cusp forms 3712 960 2752
Eisenstein series 256 0 256

Trace form

\( 960 q + 4 q^{7} + O(q^{10}) \) \( 960 q + 4 q^{7} - 8 q^{15} + 4 q^{23} + 8 q^{25} + 36 q^{33} - 24 q^{35} - 8 q^{37} + 40 q^{39} - 64 q^{43} + 192 q^{45} + 64 q^{53} - 64 q^{57} + 120 q^{59} + 68 q^{63} - 12 q^{65} + 16 q^{67} + 48 q^{73} + 48 q^{75} - 4 q^{77} - 120 q^{81} + 40 q^{85} + 12 q^{87} - 120 q^{93} + 96 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1400, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1400, [\chi])\) into lower level spaces

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