Properties

Label 400.2.be
Level $400$
Weight $2$
Character orbit 400.be
Rep. character $\chi_{400}(21,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $464$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.be (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(400, [\chi])\).

Total New Old
Modular forms 496 496 0
Cusp forms 464 464 0
Eisenstein series 32 32 0

Trace form

\( 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8} + O(q^{10}) \) \( 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8} - 14 q^{10} - 6 q^{11} + 10 q^{12} - 6 q^{13} + 6 q^{14} - 16 q^{15} - 6 q^{16} - 12 q^{17} - 24 q^{18} - 6 q^{19} - 22 q^{20} + 12 q^{21} + 10 q^{22} - 16 q^{24} + 4 q^{26} - 18 q^{27} + 18 q^{28} - 6 q^{29} - 6 q^{30} + 12 q^{31} - 36 q^{32} - 12 q^{33} - 30 q^{34} + 44 q^{35} - 82 q^{36} - 6 q^{37} - 76 q^{38} - 52 q^{40} - 10 q^{42} - 48 q^{43} + 36 q^{44} - 12 q^{45} - 14 q^{46} - 12 q^{47} - 116 q^{48} - 400 q^{49} + 10 q^{50} - 4 q^{51} + 32 q^{52} - 6 q^{53} - 30 q^{54} + 36 q^{56} + 26 q^{58} - 6 q^{59} + 48 q^{60} - 6 q^{61} - 34 q^{62} + 72 q^{63} - 24 q^{64} + 16 q^{65} + 92 q^{66} + 30 q^{67} + 28 q^{68} - 18 q^{69} + 60 q^{70} + 22 q^{72} + 28 q^{74} - 26 q^{75} - 76 q^{76} + 36 q^{77} + 14 q^{78} - 52 q^{79} - 34 q^{80} + 72 q^{81} + 56 q^{82} - 46 q^{83} + 112 q^{84} + 2 q^{85} - 46 q^{86} - 136 q^{88} - 42 q^{90} + 36 q^{91} - 4 q^{93} + 50 q^{94} - 40 q^{95} - 66 q^{96} - 12 q^{97} - 8 q^{98} - 40 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(400, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
400.2.be.a \(464\) \(3.194\) None \(-6\) \(-6\) \(-8\) \(0\)