Properties

Label 630.2.t
Level $630$
Weight $2$
Character orbit 630.t
Rep. character $\chi_{630}(311,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $3$
Sturm bound $288$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(11\)

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

\( 64 q + 32 q^{4} - 4 q^{7} + 6 q^{9} + O(q^{10}) \) \( 64 q + 32 q^{4} - 4 q^{7} + 6 q^{9} + 12 q^{13} + 6 q^{14} + 4 q^{15} - 32 q^{16} - 8 q^{18} + 22 q^{21} + 6 q^{24} + 64 q^{25} + 24 q^{26} + 36 q^{27} + 4 q^{28} - 6 q^{29} + 4 q^{30} - 12 q^{31} + 24 q^{33} + 4 q^{37} + 36 q^{39} - 6 q^{41} - 32 q^{42} + 4 q^{43} - 12 q^{44} + 6 q^{45} - 6 q^{46} + 36 q^{47} - 8 q^{49} + 8 q^{51} - 72 q^{53} - 36 q^{54} - 12 q^{57} - 60 q^{59} + 8 q^{60} + 102 q^{61} - 80 q^{63} - 64 q^{64} - 12 q^{65} - 48 q^{66} - 28 q^{67} - 6 q^{70} + 8 q^{72} - 12 q^{77} + 16 q^{78} + 8 q^{79} - 38 q^{81} + 14 q^{84} + 12 q^{85} + 96 q^{87} + 6 q^{89} + 24 q^{91} - 36 q^{92} + 8 q^{93} + 6 q^{96} + 12 q^{97} - 48 q^{98} - 48 q^{99} + O(q^{100}) \)

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.t.a 630.t 63.s $4$ $5.031$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
630.2.t.b 630.t 63.s $28$ $5.031$ None \(0\) \(-2\) \(-28\) \(-4\) $\mathrm{SU}(2)[C_{6}]$
630.2.t.c 630.t 63.s $32$ $5.031$ None \(0\) \(2\) \(32\) \(-2\) $\mathrm{SU}(2)[C_{6}]$

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

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