Properties

Label 620.2.bf
Level $620$
Weight $2$
Character orbit 620.bf
Rep. character $\chi_{620}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $64$
Newform subspaces $2$
Sturm bound $192$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 620 = 2^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 620.bf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(620, [\chi])\).

Total New Old
Modular forms 408 64 344
Cusp forms 360 64 296
Eisenstein series 48 0 48

Trace form

\( 64 q + 4 q^{7} - 24 q^{21} - 2 q^{25} + 28 q^{31} - 40 q^{33} - 12 q^{35} + 36 q^{37} + 4 q^{41} + 12 q^{43} - 14 q^{45} + 16 q^{47} + 8 q^{51} + 12 q^{53} - 54 q^{55} + 24 q^{57} + 60 q^{63} - 48 q^{65}+ \cdots - 20 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(620, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
620.2.bf.a 620.bf 155.p $4$ $4.951$ \(\Q(\zeta_{12})\) None 620.2.bf.a \(0\) \(6\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12}+\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+(-\zeta_{12}+\cdots)q^{5}+\cdots\)
620.2.bf.b 620.bf 155.p $60$ $4.951$ None 620.2.bf.b \(0\) \(-6\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(620, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(620, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)