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Properties

Label 420.2.bo
Level $420$
Weight $2$
Character orbit 420.bo
Rep. character $\chi_{420}(73,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $32$
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.bo (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 432 32 400
Cusp forms 336 32 304
Eisenstein series 96 0 96

Trace form

\( 32 q - 12 q^{5} + 8 q^{11} + 8 q^{15} - 8 q^{21} + 16 q^{23} - 4 q^{25} + 24 q^{31} + 12 q^{33} + 20 q^{35} + 20 q^{37} - 24 q^{43} + 12 q^{47} - 8 q^{51} + 40 q^{53} - 16 q^{57} - 24 q^{61} - 12 q^{63}+ \cdots - 36 q^{95}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
420.2.bo.a 420.bo 35.k $32$ $3.354$ None 420.2.bo.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(420, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(420, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)