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Properties

Label 630.2.m
Level $630$
Weight $2$
Character orbit 630.m
Rep. character $\chi_{630}(197,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $4$
Sturm bound $288$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(11\), \(17\)

Dimensions

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

Total New Old
Modular forms 320 24 296
Cusp forms 256 24 232
Eisenstein series 64 0 64

Trace form

\( 24 q + O(q^{10}) \) \( 24 q + 24 q^{13} - 24 q^{16} - 16 q^{22} + 16 q^{25} + 32 q^{31} + 8 q^{37} + 8 q^{40} - 32 q^{43} - 32 q^{46} - 24 q^{52} - 32 q^{55} + 8 q^{58} + 96 q^{67} - 16 q^{70} + 72 q^{73} - 8 q^{82} + 48 q^{85} - 16 q^{88} - 56 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
630.2.m.a 630.m 15.e $4$ $5.031$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2-\zeta_{8}^{2})q^{5}+\cdots\)
630.2.m.b 630.m 15.e $4$ $5.031$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(2+\zeta_{8}^{2})q^{5}+\zeta_{8}^{3}q^{7}+\cdots\)
630.2.m.c 630.m 15.e $8$ $5.031$ 8.0.1698758656.6 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{5}q^{4}+(-\beta _{1}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
630.2.m.d 630.m 15.e $8$ $5.031$ 8.0.1698758656.6 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}-\beta _{5}q^{4}+(-\beta _{2}-\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)