Properties

Label 630.2.d
Level 630
Weight 2
Character orbit d
Rep. character \(\chi_{630}(629,\cdot)\)
Character field \(\Q\)
Dimension 16
Newforms 4
Sturm bound 288
Trace bound 23

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Defining parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 630.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(11\), \(23\)

Dimensions

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

Total New Old
Modular forms 160 16 144
Cusp forms 128 16 112
Eisenstein series 32 0 32

Trace form

\(16q \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut +\mathstrut 16q^{46} \) \(\mathstrut +\mathstrut 8q^{49} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut +\mathstrut 40q^{70} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut -\mathstrut 40q^{91} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.d.a \(4\) \(5.031\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
630.2.d.b \(4\) \(5.031\) \(\Q(\sqrt{-2}, \sqrt{5})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
630.2.d.c \(4\) \(5.031\) \(\Q(\sqrt{-2}, \sqrt{5})\) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
630.2.d.d \(4\) \(5.031\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)