Space of modular forms of level 1470, weight 2, and Character 1470.m

• Label: 1470.2.m
• Level: $1470$
• Weight: $2$
• Character orbit: 1470.m
• Rep. character: $\chi_{1470}(97,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $672$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(672\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1470, [\chi])\).

	Total	New	Old
Modular forms	736	80	656
Cusp forms	608	80	528
Eisenstein series	128	0	128

Trace form

\( 80 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1470, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1470.2.m.a	$1470$	$2$	1470.m	35.f	$4$	$8$	$4$	$11.738$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2\cdot 7^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{3}q^{3}-\zeta_{16}^{2}q^{4}+\cdots\)
1470.2.m.b	$1470$	$2$	1470.m	35.f	$4$	$8$	$4$	$11.738$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2\cdot 7^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{3}q^{3}-\zeta_{16}^{2}q^{4}+\cdots\)
1470.2.m.c	$1470$	$2$	1470.m	35.f	$4$	$16$	$8$	$11.738$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}-\beta _{6}q^{3}-\beta _{5}q^{4}+\beta _{3}q^{5}+\cdots\)
1470.2.m.d	$1470$	$2$	1470.m	35.f	$4$	$16$	$8$	$11.738$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{10}q^{2}-\beta _{10}q^{3}-\beta _{8}q^{4}+(1+2\beta _{1}+\cdots)q^{5}+\cdots\)
1470.2.m.e	$1470$	$2$	1470.m	35.f	$4$	$16$	$8$	$11.738$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{10}q^{2}+\beta _{10}q^{3}-\beta _{8}q^{4}+(-1+\cdots)q^{5}+\cdots\)
1470.2.m.f	$1470$	$2$	1470.m	35.f	$4$	$16$	$8$	$11.738$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}+\beta _{6}q^{3}-\beta _{5}q^{4}-\beta _{3}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1470, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)