Properties

Label 630.2.bl
Level $630$
Weight $2$
Character orbit 630.bl
Rep. character $\chi_{630}(41,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $2$
Sturm bound $288$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(13\)

Dimensions

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

Total New Old
Modular forms 304 64 240
Cusp forms 272 64 208
Eisenstein series 32 0 32

Trace form

\( 64 q + 32 q^{4} - 4 q^{7} - 12 q^{9} + O(q^{10}) \) \( 64 q + 32 q^{4} - 4 q^{7} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 4 q^{15} - 32 q^{16} + 16 q^{18} - 8 q^{21} + 72 q^{23} - 32 q^{25} - 8 q^{28} + 12 q^{29} + 4 q^{30} - 12 q^{36} + 16 q^{37} + 12 q^{39} + 4 q^{42} - 8 q^{43} - 24 q^{46} + 10 q^{49} - 40 q^{51} + 6 q^{56} - 72 q^{57} - 4 q^{60} + 16 q^{63} - 64 q^{64} + 12 q^{65} + 56 q^{67} - 6 q^{70} - 16 q^{72} - 72 q^{74} - 12 q^{77} + 64 q^{78} + 20 q^{79} - 20 q^{81} - 22 q^{84} + 12 q^{85} + 48 q^{86} - 48 q^{91} + 72 q^{92} + 8 q^{93} + 36 q^{99} + O(q^{100}) \)

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.bl.a 630.bl 63.o $32$ $5.031$ None \(0\) \(-4\) \(-16\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
630.2.bl.b 630.bl 63.o $32$ $5.031$ None \(0\) \(4\) \(16\) \(-2\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)