Properties

Label 630.2.ca
Level $630$
Weight $2$
Character orbit 630.ca
Rep. character $\chi_{630}(113,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $144$
Newform subspaces $2$
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.ca (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(13\)

Dimensions

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

Total New Old
Modular forms 608 144 464
Cusp forms 544 144 400
Eisenstein series 64 0 64

Trace form

\( 144 q - 8 q^{3} + O(q^{10}) \) \( 144 q - 8 q^{3} + 24 q^{11} + 8 q^{12} - 8 q^{15} + 72 q^{16} + 8 q^{18} + 24 q^{20} + 8 q^{21} + 24 q^{23} + 24 q^{25} + 16 q^{27} + 8 q^{33} - 8 q^{36} + 48 q^{37} - 72 q^{38} - 96 q^{41} - 80 q^{45} - 96 q^{47} - 16 q^{48} + 32 q^{51} + 48 q^{55} - 32 q^{57} - 8 q^{63} + 24 q^{65} + 16 q^{66} + 24 q^{67} + 16 q^{72} - 32 q^{75} + 32 q^{78} + 96 q^{82} - 120 q^{83} + 48 q^{85} + 144 q^{86} - 40 q^{87} - 40 q^{90} - 48 q^{91} + 24 q^{92} - 32 q^{93} - 120 q^{95} + 72 q^{97} + O(q^{100}) \)

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.ca.a 630.ca 45.l $72$ $5.031$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
630.2.ca.b 630.ca 45.l $72$ $5.031$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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