Properties

Label 630.4.bo
Level $630$
Weight $4$
Character orbit 630.bo
Rep. character $\chi_{630}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $2$
Sturm bound $576$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 630.bo (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(630, [\chi])\).

Total New Old
Modular forms 896 96 800
Cusp forms 832 96 736
Eisenstein series 64 0 64

Trace form

\( 96 q - 192 q^{4} + O(q^{10}) \) \( 96 q - 192 q^{4} + 72 q^{10} - 768 q^{16} - 864 q^{19} + 156 q^{25} + 1656 q^{31} - 288 q^{40} - 864 q^{46} + 1176 q^{49} + 5184 q^{61} + 6144 q^{64} + 1128 q^{70} - 1512 q^{79} - 1920 q^{85} - 8952 q^{91} + 1296 q^{94} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(630, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
630.4.bo.a 630.bo 105.p $48$ $37.171$ None \(-48\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{6}]$
630.4.bo.b 630.bo 105.p $48$ $37.171$ None \(48\) \(0\) \(18\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

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