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Properties

Label 630.2.bk
Level $630$
Weight $2$
Character orbit 630.bk
Rep. character $\chi_{630}(101,\cdot)$
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.bk (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

\( 64 q - 64 q^{4} - 4 q^{7} + O(q^{10}) \) \( 64 q - 64 q^{4} - 4 q^{7} - 12 q^{11} - 12 q^{13} + 6 q^{14} + 4 q^{15} + 64 q^{16} + 16 q^{18} + 16 q^{21} + 36 q^{23} - 32 q^{25} - 24 q^{26} - 36 q^{27} + 4 q^{28} - 6 q^{29} - 2 q^{30} + 4 q^{37} - 12 q^{39} + 6 q^{41} + 28 q^{42} + 4 q^{43} + 12 q^{44} + 6 q^{45} - 6 q^{46} + 72 q^{47} + 10 q^{49} - 40 q^{51} + 12 q^{52} + 72 q^{53} - 36 q^{54} - 6 q^{56} - 12 q^{57} - 120 q^{59} - 4 q^{60} + 28 q^{63} - 64 q^{64} - 48 q^{66} + 56 q^{67} + 12 q^{70} - 16 q^{72} - 36 q^{74} - 12 q^{77} + 16 q^{78} - 16 q^{79} + 40 q^{81} - 16 q^{84} + 12 q^{85} - 48 q^{86} + 12 q^{87} - 6 q^{89} + 24 q^{91} - 36 q^{92} - 28 q^{93} - 12 q^{97} + 48 q^{98} - 48 q^{99} + O(q^{100}) \)

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.bk.a 630.bk 63.i $4$ $5.031$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}^{3}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-q^{4}+\cdots\)
630.2.bk.b 630.bk 63.i $28$ $5.031$ None \(0\) \(2\) \(-14\) \(8\) $\mathrm{SU}(2)[C_{6}]$
630.2.bk.c 630.bk 63.i $32$ $5.031$ None \(0\) \(-2\) \(16\) \(-2\) $\mathrm{SU}(2)[C_{6}]$

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

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