Space of modular forms of level 3528, weight 2, and Character 3528.s

• Label: 3528.2.s
• Level: $3528$
• Weight: $2$
• Character orbit: 3528.s
• Rep. character: $\chi_{3528}(361,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $100$
• Newform subspaces: $39$
• Sturm bound: $1344$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3528.s (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 39 \)
Sturm bound:			\(1344\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3528, [\chi])\).

	Total	New	Old
Modular forms	1472	100	1372
Cusp forms	1216	100	1116
Eisenstein series	256	0	256

Trace form

\( 100 q + 2 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3528, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3528.2.s.a	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{17}+2\zeta_{6}q^{19}+\cdots\)
3528.2.s.b	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\zeta_{6}q^{5}+3q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
3528.2.s.c	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(-6+6\zeta_{6})q^{11}-6q^{13}+\cdots\)
3528.2.s.d	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(-6+6\zeta_{6})q^{11}+3q^{13}+\cdots\)
3528.2.s.e	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.f	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{11}+2q^{13}+\cdots\)
3528.2.s.g	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}-6q^{13}+(2-2\zeta_{6})q^{17}+\cdots\)
3528.2.s.h	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+2q^{13}+(-6+6\zeta_{6})q^{17}+\cdots\)
3528.2.s.i	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.j	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.k	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(6-6\zeta_{6})q^{11}+6q^{13}+\cdots\)
3528.2.s.l	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-5+5\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.m	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-4q^{13}+(-4+4\zeta_{6})q^{17}-4\zeta_{6}q^{19}+\cdots\)
3528.2.s.n	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+4q^{13}+(4-4\zeta_{6})q^{17}+4\zeta_{6}q^{19}+\cdots\)
3528.2.s.o	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.p	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{11}-4q^{13}-4\zeta_{6}q^{19}+\cdots\)
3528.2.s.q	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{11}+6q^{13}+(5+\cdots)q^{17}+\cdots\)
3528.2.s.r	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(5-5\zeta_{6})q^{11}-2q^{13}+(-6+\cdots)q^{17}+\cdots\)
3528.2.s.s	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(-6+6\zeta_{6})q^{11}+6q^{13}+\cdots\)
3528.2.s.t	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+2q^{13}+\cdots\)
3528.2.s.u	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.v	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}-2q^{13}+(6-6\zeta_{6})q^{17}+\cdots\)
3528.2.s.w	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+6q^{13}+(-2+2\zeta_{6})q^{17}+\cdots\)
3528.2.s.x	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{11}+2q^{13}+\cdots\)
3528.2.s.y	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+2q^{13}+\cdots\)
3528.2.s.z	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(6-6\zeta_{6})q^{11}-6q^{13}+\cdots\)
3528.2.s.ba	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{17}-2\zeta_{6}q^{19}+\cdots\)
3528.2.s.bb	$3528$	$2$	3528.s	7.c	$3$	$2$	$1$	$28.171$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\zeta_{6}q^{5}+3q^{13}+(-4+4\zeta_{6})q^{17}+\cdots\)
3528.2.s.bc	$3528$	$2$	3528.s	7.c	$3$	$4$	$2$	$28.171$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+(-2-2\beta _{1}+\cdots)q^{11}+\cdots\)
3528.2.s.bd	$3528$	$2$	3528.s	7.c	$3$	$4$	$2$	$28.171$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+(2-2\beta _{1}+\cdots)q^{11}+\cdots\)
3528.2.s.be	$3528$	$2$	3528.s	7.c	$3$	$4$	$2$	$28.171$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{5}+4\beta _{2}q^{11}+\beta _{3}q^{13}+(2\beta _{1}+\cdots)q^{17}+\cdots\)
3528.2.s.bf	$3528$	$2$	3528.s	7.c	$3$	$4$	$2$	$28.171$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{5}+2\beta _{2}q^{11}+2\beta _{3}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
3528.2.s.bg	$3528$	$2$	3528.s	7.c	$3$	$4$	$2$	$28.171$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{5}+\beta _{3}q^{13}+(\beta _{1}+\beta _{3})q^{17}+\cdots\)
3528.2.s.bh	$3528$	$2$	3528.s	7.c	$3$	$4$	$2$	$28.171$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{5}-\beta _{3}q^{13}+(\beta _{1}+\beta _{3})q^{17}+\cdots\)
3528.2.s.bi	$3528$	$2$	3528.s	7.c	$3$	$4$	$2$	$28.171$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{5}-2\beta _{2}q^{11}-2\beta _{3}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
3528.2.s.bj	$3528$	$2$	3528.s	7.c	$3$	$4$	$2$	$28.171$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{1}q^{5}-6\beta _{2}q^{11}+4\beta _{3}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
3528.2.s.bk	$3528$	$2$	3528.s	7.c	$3$	$4$	$2$	$28.171$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{5}+(-\beta _{2}+\beta _{3})q^{11}+(-3+\beta _{2}+\cdots)q^{13}+\cdots\)
3528.2.s.bl	$3528$	$2$	3528.s	7.c	$3$	$4$	$2$	$28.171$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(-2+2\beta _{1}+\cdots)q^{11}+\cdots\)
3528.2.s.bm	$3528$	$2$	3528.s	7.c	$3$	$4$	$2$	$28.171$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(2+2\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)