Properties

Label 1400.2.z
Level $1400$
Weight $2$
Character orbit 1400.z
Rep. character $\chi_{1400}(281,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $184$
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.z (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 992 184 808
Cusp forms 928 184 744
Eisenstein series 64 0 64

Trace form

\( 184 q + 2 q^{5} - 50 q^{9} + O(q^{10}) \) \( 184 q + 2 q^{5} - 50 q^{9} + 12 q^{11} - 4 q^{13} + 28 q^{15} + 4 q^{17} - 4 q^{21} - 8 q^{23} - 6 q^{25} + 24 q^{27} - 16 q^{29} - 24 q^{33} - 50 q^{37} + 12 q^{39} - 4 q^{41} + 70 q^{45} + 48 q^{47} + 184 q^{49} - 96 q^{51} + 18 q^{53} + 56 q^{55} + 16 q^{57} + 20 q^{61} + 12 q^{63} - 6 q^{65} + 48 q^{67} + 24 q^{69} + 24 q^{71} - 4 q^{73} - 8 q^{75} - 98 q^{81} - 40 q^{83} - 62 q^{85} - 12 q^{87} + 6 q^{89} + 12 q^{91} - 96 q^{93} - 80 q^{95} - 28 q^{97} - 184 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)