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

• Label: 1470.2.b
• Level: $1470$
• Weight: $2$
• Character orbit: 1470.b
• Rep. character: $\chi_{1470}(881,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $672$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(672\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	368	56	312
Cusp forms	304	56	248
Eisenstein series	64	0	64

Trace form

\( 56 q - 56 q^{4} + 4 q^{9} + O(q^{10}) \)

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.b.a	$1470$	$2$	1470.b	21.c	$2$	$12$	$12$	$11.738$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(12\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-\beta _{1}q^{3}-q^{4}+q^{5}-\beta _{9}q^{6}+\cdots\)
1470.2.b.b	$1470$	$2$	1470.b	21.c	$2$	$12$	$12$	$11.738$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(-12\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+\beta _{1}q^{3}-q^{4}-q^{5}+\beta _{9}q^{6}+\cdots\)
1470.2.b.c	$1470$	$2$	1470.b	21.c	$2$	$16$	$16$	$11.738$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(-8\)	\(-16\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{2}-\beta _{11}q^{3}-q^{4}-q^{5}+(-\beta _{5}+\cdots)q^{6}+\cdots\)
1470.2.b.d	$1470$	$2$	1470.b	21.c	$2$	$16$	$16$	$11.738$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(8\)	\(16\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{2}+\beta _{11}q^{3}-q^{4}+q^{5}+(\beta _{5}+\cdots)q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)