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

• Label: 1470.2.i
• Level: $1470$
• Weight: $2$
• Character orbit: 1470.i
• Rep. character: $\chi_{1470}(361,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $56$
• Newform subspaces: $24$
• 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.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(672\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\), \(31\)

Dimensions

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

	Total	New	Old
Modular forms	736	56	680
Cusp forms	608	56	552
Eisenstein series	128	0	128

Trace form

56 * q - 28 * q^4 - 28 * q^9 + 4 * q^10 - 4 * q^11 - 16 * q^13 - 28 * q^16 - 8 * q^17 - 4 * q^19 + 16 * q^22 - 28 * q^25 - 4 * q^26 + 32 * q^29 - 8 * q^31 + 8 * q^33 + 16 * q^34 + 56 * q^36 - 48 * q^37 - 8 * q^38 - 40 * q^39 + 4 * q^40 - 24 * q^41 + 48 * q^43 - 4 * q^44 + 12 * q^46 - 16 * q^47 + 8 * q^51 + 8 * q^52 - 24 * q^53 + 16 * q^55 + 80 * q^57 + 8 * q^58 + 32 * q^59 + 8 * q^61 - 32 * q^62 + 56 * q^64 - 4 * q^65 - 40 * q^67 - 8 * q^68 + 32 * q^69 + 32 * q^71 - 8 * q^73 - 4 * q^74 + 8 * q^76 - 32 * q^78 - 56 * q^79 - 28 * q^81 + 16 * q^82 - 16 * q^83 + 16 * q^85 - 8 * q^88 + 8 * q^89 - 8 * q^90 - 56 * q^93 - 12 * q^94 + 64 * q^97 + 8 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1470.2.i.a	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.a.e	$2$	$0$	\(-1\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.b	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.a.c	$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.c	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None		✓			1470.2.a.n	$2$	$1$	\(-1\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.d	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.a.d	$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.e	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.i.b	$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.f	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.a.c	$2$	$0$	\(-1\)	\(1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.g	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None		✓			1470.2.a.n	$2$	$0$	\(-1\)	\(1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.h	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.a.d	$2$	$1$	\(-1\)	\(1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.i	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.i.a	$2$	$1$	\(-1\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.j	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.a.e	$2$	$0$	\(-1\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.k	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None		✓			1470.2.a.c	$2$	$0$	\(1\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.l	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.a.b	$2$	$0$	\(1\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.m	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.i.d	$2$	$0$	\(1\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.n	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.a.a	$2$	$0$	\(1\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.o	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					30.2.a.a	$2$	$0$	\(1\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.p	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.i.c	$2$	$0$	\(1\)	\(1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.q	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					30.2.a.a	$2$	$0$	\(1\)	\(1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.r	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None		✓			1470.2.a.c	$2$	$0$	\(1\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.s	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.a.b	$2$	$0$	\(1\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.t	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	\(\Q(\sqrt{-3}) \)	None					210.2.a.a	$2$	$0$	\(1\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.u	$1470$	$2$	1470.i	7.c	$3$	$4$	$2$	$11.738$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			1470.2.a.u	$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
1470.2.i.v	$1470$	$2$	1470.i	7.c	$3$	$4$	$2$	$11.738$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			1470.2.a.u	$2$	$0$	\(-2\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
1470.2.i.w	$1470$	$2$	1470.i	7.c	$3$	$4$	$2$	$11.738$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			1470.2.a.s	$2$	$0$	\(2\)	\(-2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
1470.2.i.x	$1470$	$2$	1470.i	7.c	$3$	$4$	$2$	$11.738$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			1470.2.a.s	$2$	$0$	\(2\)	\(2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)