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Properties

Label 1400.2.cm
Level $1400$
Weight $2$
Character orbit 1400.cm
Rep. character $\chi_{1400}(81,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $480$
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.cm (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1984 480 1504
Cusp forms 1856 480 1376
Eisenstein series 128 0 128

Trace form

\( 480 q - 4 q^{7} + 60 q^{9} + O(q^{10}) \) \( 480 q - 4 q^{7} + 60 q^{9} - 36 q^{15} + 12 q^{19} + 10 q^{23} - 10 q^{25} - 24 q^{27} - 6 q^{31} - 12 q^{33} - 4 q^{35} - 8 q^{37} + 12 q^{39} + 32 q^{41} + 64 q^{43} - 32 q^{45} + 12 q^{49} + 12 q^{51} + 24 q^{53} + 4 q^{55} + 96 q^{57} + 24 q^{59} - 12 q^{61} + 68 q^{63} + 10 q^{65} + 16 q^{67} + 32 q^{69} - 22 q^{75} + 20 q^{77} + 16 q^{79} + 24 q^{81} - 4 q^{83} - 84 q^{85} + 4 q^{87} - 24 q^{89} - 16 q^{91} - 72 q^{93} - 62 q^{95} - 60 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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