Properties

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

Related objects

Downloads

Learn more about

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: \(\Q(\zeta_{6})\)
Newforms: \( 3 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(630, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
630.2.t.a \(4\) \(5.031\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(2\) \(q-\zeta_{12}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
630.2.t.b \(28\) \(5.031\) None \(0\) \(-2\) \(-28\) \(-4\)
630.2.t.c \(32\) \(5.031\) None \(0\) \(2\) \(32\) \(-2\)

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

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