Space of modular forms of level 1470, weight 3, and Character 1470.f

• Label: 1470.3.f
• Level: $1470$
• Weight: $3$
• Character orbit: 1470.f
• Rep. character: $\chi_{1470}(391,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $1008$
• Trace bound: $22$

Defining parameters

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1470.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1008\)
Trace bound:			\(22\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1470, [\chi])\).

	Total	New	Old
Modular forms	704	56	648
Cusp forms	640	56	584
Eisenstein series	64	0	64

Trace form

\( 56 q + 112 q^{4} - 168 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1470, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1470.3.f.a	$1470$	$3$	1470.f	7.b	$2$	$8$	$8$	$40.055$	8.0.3317760000.3	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+2q^{4}+\beta _{6}q^{5}+\beta _{3}q^{6}+\cdots\)
1470.3.f.b	$1470$	$3$	1470.f	7.b	$2$	$16$	$16$	$40.055$	16.0.\(\cdots\).5	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+2q^{4}+\beta _{7}q^{5}-\beta _{3}q^{6}+\cdots\)
1470.3.f.c	$1470$	$3$	1470.f	7.b	$2$	$16$	$16$	$40.055$	16.0.\(\cdots\).5	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+2q^{4}-\beta _{7}q^{5}-\beta _{4}q^{6}+\cdots\)
1470.3.f.d	$1470$	$3$	1470.f	7.b	$2$	$16$	$16$	$40.055$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+2q^{4}-\beta _{7}q^{5}-\beta _{8}q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1470, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)