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

• Label: 1470.2.g
• Level: $1470$
• Weight: $2$
• Character orbit: 1470.g
• Rep. character: $\chi_{1470}(589,\cdot)$
• Character field: $\Q$
• Dimension: $42$
• Newform subspaces: $11$
• Sturm bound: $672$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(672\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(11\), \(17\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	368	42	326
Cusp forms	304	42	262
Eisenstein series	64	0	64

Trace form

\( 42 q - 42 q^{4} + 4 q^{5} - 2 q^{6} - 42 q^{9} + O(q^{10}) \)

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.g.a	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+(-2-i)q^{5}+\cdots\)
1470.2.g.b	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
1470.2.g.c	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
1470.2.g.d	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+(1-2i)q^{5}+q^{6}+\cdots\)
1470.2.g.e	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+(1-2i)q^{5}+q^{6}+\cdots\)
1470.2.g.f	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\cdots\)
1470.2.g.g	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}-q^{6}+\cdots\)
1470.2.g.h	$1470$	$2$	1470.g	5.b	$2$	$6$	$6$	$11.738$	6.0.29160000.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}-\beta _{2}q^{5}-q^{6}+\cdots\)
1470.2.g.i	$1470$	$2$	1470.g	5.b	$2$	$6$	$6$	$11.738$	6.0.29160000.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{5}+q^{6}+\cdots\)
1470.2.g.j	$1470$	$2$	1470.g	5.b	$2$	$8$	$8$	$11.738$	8.0.1698758656.6	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{5}q^{3}-q^{4}+(-1+\beta _{7})q^{5}+\cdots\)
1470.2.g.k	$1470$	$2$	1470.g	5.b	$2$	$8$	$8$	$11.738$	8.0.1698758656.6	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+\beta _{5}q^{3}-q^{4}+(1-\beta _{7})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)