Properties

Label 400.2.bm
Level $400$
Weight $2$
Character orbit 400.bm
Rep. character $\chi_{400}(67,\cdot)$
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.bm (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

\( 464 q - 8 q^{2} - 10 q^{3} - 10 q^{4} - 8 q^{5} - 6 q^{6} - 16 q^{7} - 2 q^{8} + 108 q^{9} - 4 q^{10} - 6 q^{11} - 22 q^{12} - 6 q^{13} - 10 q^{14} - 12 q^{15} + 34 q^{16} - 16 q^{17} - 24 q^{18} - 10 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
400.2.bm.a 400.bm 400.am $464$ $3.194$ None 400.2.bd.a \(-8\) \(-10\) \(-8\) \(-16\) $\mathrm{SU}(2)[C_{20}]$