Properties

Label 630.2.d
Level $630$
Weight $2$
Character orbit 630.d
Rep. character $\chi_{630}(629,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $4$
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: \(\Q\)
Newform subspaces: \( 4 \)
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

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

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.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

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