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

• Label: 1470.2.d
• Level: $1470$
• Weight: $2$
• Character orbit: 1470.d
• Rep. character: $\chi_{1470}(1469,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $8$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(672\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\), \(13\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	368	80	288
Cusp forms	304	80	224
Eisenstein series	64	0	64

Trace form

\( 80 q + 80 q^{4} + 4 q^{9} + O(q^{10}) \)

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.d.a	$1470$	$2$	1470.d	105.g	$2$	$4$	$4$	$11.738$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(-4\)	\(-1\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1470.2.d.b	$1470$	$2$	1470.d	105.g	$2$	$4$	$4$	$11.738$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(-4\)	\(1\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1470.2.d.c	$1470$	$2$	1470.d	105.g	$2$	$4$	$4$	$11.738$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(4\)	\(-1\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
1470.2.d.d	$1470$	$2$	1470.d	105.g	$2$	$4$	$4$	$11.738$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(4\)	\(1\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(2\beta _{2}+\beta _{3})q^{5}+\cdots\)
1470.2.d.e	$1470$	$2$	1470.d	105.g	$2$	$8$	$8$	$11.738$	8.0.3317760000.3	None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(\beta _{2}+\beta _{5})q^{3}+q^{4}+(\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
1470.2.d.f	$1470$	$2$	1470.d	105.g	$2$	$8$	$8$	$11.738$	8.0.3317760000.3	None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(\beta _{2}+\beta _{5})q^{3}+q^{4}+(-\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
1470.2.d.g	$1470$	$2$	1470.d	105.g	$2$	$24$	$24$	$11.738$		None		$4$	$0$	\(-24\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1470.2.d.h	$1470$	$2$	1470.d	105.g	$2$	$24$	$24$	$11.738$		None		$4$	$0$	\(24\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)