Properties

Label 630.2.g
Level $630$
Weight $2$
Character orbit 630.g
Rep. character $\chi_{630}(379,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $7$
Sturm bound $288$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(11\), \(29\)

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

\( 16q - 16q^{4} - 4q^{5} + O(q^{10}) \) \( 16q - 16q^{4} - 4q^{5} + 4q^{14} + 16q^{16} + 16q^{19} + 4q^{20} - 12q^{25} - 8q^{26} + 8q^{29} + 32q^{31} + 4q^{35} + 8q^{41} + 8q^{46} - 16q^{49} - 12q^{50} + 8q^{55} - 4q^{56} - 48q^{59} - 48q^{61} - 16q^{64} + 20q^{65} + 4q^{70} + 64q^{71} + 16q^{74} - 16q^{76} + 40q^{79} - 4q^{80} - 16q^{85} - 8q^{86} - 40q^{89} - 8q^{91} - 4q^{95} + O(q^{100}) \)

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.g.a \(2\) \(5.031\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}-q^{4}+(-2-i)q^{5}+iq^{7}+\cdots\)
630.2.g.b \(2\) \(5.031\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}-q^{4}+(-1+2i)q^{5}-iq^{7}+\cdots\)
630.2.g.c \(2\) \(5.031\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{7}+\cdots\)
630.2.g.d \(2\) \(5.031\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-q^{4}+(1+2i)q^{5}-iq^{7}-iq^{8}+\cdots\)
630.2.g.e \(2\) \(5.031\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}-iq^{8}+\cdots\)
630.2.g.f \(2\) \(5.031\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}-q^{4}+(2-i)q^{5}-iq^{7}-iq^{8}+\cdots\)
630.2.g.g \(4\) \(5.031\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)