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Properties

Label 630.2.p
Level $630$
Weight $2$
Character orbit 630.p
Rep. character $\chi_{630}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
Newform subspaces $4$
Sturm bound $288$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(630, [\chi])\).

Total New Old
Modular forms 320 40 280
Cusp forms 256 40 216
Eisenstein series 64 0 64

Trace form

\( 40 q + O(q^{10}) \) \( 40 q - 16 q^{11} - 40 q^{16} + 16 q^{22} - 24 q^{23} + 16 q^{25} + 40 q^{35} + 16 q^{37} - 16 q^{46} - 32 q^{50} + 48 q^{53} + 24 q^{65} - 48 q^{67} + 16 q^{77} + 32 q^{85} - 16 q^{86} - 16 q^{88} + 32 q^{91} - 24 q^{92} - 64 q^{95} - 16 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(630, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
630.2.p.a 630.p 35.f $8$ $5.031$ \(\Q(\zeta_{16})\) None 70.2.g.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{16}^{2}q^{2}+\zeta_{16}^{4}q^{4}+(-\zeta_{16}-2\zeta_{16}^{5}+\cdots)q^{5}+\cdots\)
630.2.p.b 630.p 35.f $8$ $5.031$ 8.0.1698758656.6 None 210.2.m.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}-\beta _{5}q^{4}+(-\beta _{1}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
630.2.p.c 630.p 35.f $8$ $5.031$ 8.0.1698758656.6 None 210.2.m.a \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{5}q^{4}+(-\beta _{2}-\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots\)
630.2.p.d 630.p 35.f $16$ $5.031$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 630.2.p.d \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}-\beta _{9}q^{4}-\beta _{12}q^{5}-\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(630, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)