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Properties

Label 420.2.br
Level $420$
Weight $2$
Character orbit 420.br
Rep. character $\chi_{420}(47,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $352$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 420.br (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 420 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(420, [\chi])\).

Total New Old
Modular forms 416 416 0
Cusp forms 352 352 0
Eisenstein series 64 64 0

Trace form

\( 352 q + O(q^{10}) \) \( 352 q - 12 q^{10} - 6 q^{12} - 8 q^{16} + 6 q^{18} - 8 q^{21} - 8 q^{25} - 24 q^{28} - 32 q^{30} - 12 q^{33} - 48 q^{36} - 8 q^{37} - 72 q^{40} - 26 q^{42} - 12 q^{45} - 8 q^{46} - 60 q^{52} - 72 q^{57} - 52 q^{58} + 10 q^{60} - 48 q^{61} + 60 q^{66} - 104 q^{70} - 38 q^{72} - 24 q^{73} - 56 q^{78} - 48 q^{81} - 96 q^{82} - 32 q^{85} - 12 q^{88} + 20 q^{93} + 72 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(420, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
420.2.br.a 420.br 420.ar $352$ $3.354$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$