Properties

Label 630.2.i
Level 630
Weight 2
Character orbit i
Rep. character \(\chi_{630}(121,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 64
Newform subspaces 9
Sturm bound 288
Trace bound 5

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Defining parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 630.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 9 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(11\), \(13\)

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

\( 64q + 64q^{4} + 4q^{5} + 4q^{6} + 4q^{7} + 8q^{9} + O(q^{10}) \) \( 64q + 64q^{4} + 4q^{5} + 4q^{6} + 4q^{7} + 8q^{9} - 4q^{11} - 4q^{13} - 2q^{14} + 4q^{15} + 64q^{16} + 16q^{17} + 16q^{18} + 8q^{19} + 4q^{20} + 24q^{21} + 12q^{23} + 4q^{24} - 32q^{25} + 8q^{26} - 12q^{27} + 4q^{28} + 10q^{29} - 2q^{30} + 8q^{31} + 40q^{33} + 8q^{36} - 4q^{37} + 24q^{38} - 4q^{39} - 22q^{41} - 4q^{42} - 4q^{43} - 4q^{44} - 2q^{45} + 6q^{46} - 24q^{47} - 2q^{49} - 48q^{51} - 4q^{52} - 8q^{53} - 20q^{54} - 2q^{56} - 52q^{57} - 40q^{59} + 4q^{60} + 44q^{61} - 64q^{62} + 12q^{63} + 64q^{64} + 8q^{65} + 56q^{67} + 16q^{68} - 56q^{69} + 12q^{70} - 88q^{71} + 16q^{72} + 56q^{73} + 12q^{74} + 8q^{76} - 100q^{77} - 48q^{78} + 32q^{79} + 4q^{80} + 8q^{81} + 24q^{83} + 24q^{84} - 12q^{85} - 20q^{86} - 60q^{87} + 2q^{89} + 32q^{91} + 12q^{92} + 12q^{93} + 24q^{94} + 4q^{96} - 4q^{97} + 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(630, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
630.2.i.a \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(-1\) \(-1\) \(q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
630.2.i.b \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(1\) \(-4\) \(q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
630.2.i.c \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-1\) \(-5\) \(q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
630.2.i.d \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(1\) \(-4\) \(q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
630.2.i.e \(4\) \(5.031\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(-6\) \(2\) \(-2\) \(q+q^{2}+(-2-\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
630.2.i.f \(12\) \(5.031\) 12.0.\(\cdots\).1 None \(-12\) \(2\) \(-6\) \(4\) \(q-q^{2}+(\beta _{4}-\beta _{7})q^{3}+q^{4}+(-1+\beta _{6}+\cdots)q^{5}+\cdots\)
630.2.i.g \(12\) \(5.031\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(0\) \(-6\) \(4\) \(q+q^{2}-\beta _{8}q^{3}+q^{4}+(-1-\beta _{6})q^{5}+\cdots\)
630.2.i.h \(12\) \(5.031\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(2\) \(6\) \(8\) \(q+q^{2}+(-\beta _{2}+\beta _{6})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
630.2.i.i \(16\) \(5.031\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(2\) \(8\) \(4\) \(q-q^{2}+(-\beta _{1}+\beta _{7})q^{3}+q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)

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

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