Properties

Label 630.2.bt
Level 630
Weight 2
Character orbit bt
Rep. character \(\chi_{630}(317,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 192
Newforms 1
Sturm bound 288
Trace bound 0

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Defining parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 630.bt (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Newforms: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 608 192 416
Cusp forms 544 192 352
Eisenstein series 64 0 64

Trace form

\(192q \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(192q \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 96q^{16} \) \(\mathstrut +\mathstrut 36q^{17} \) \(\mathstrut +\mathstrut 16q^{18} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 36q^{27} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 20q^{33} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut -\mathstrut 48q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 48q^{57} \) \(\mathstrut +\mathstrut 24q^{58} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 8q^{72} \) \(\mathstrut -\mathstrut 88q^{75} \) \(\mathstrut -\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut +\mathstrut 40q^{87} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.bt.a \(192\) \(5.031\) None \(0\) \(0\) \(0\) \(0\)

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

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