Space of modular forms of level 735, weight 2, and Character 735.j

• Label: 735.2.j
• Level: $735$
• Weight: $2$
• Character orbit: 735.j
• Rep. character: $\chi_{735}(197,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $144$
• Newform subspaces: $8$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(735, [\chi])\).

	Total	New	Old
Modular forms	256	184	72
Cusp forms	192	144	48
Eisenstein series	64	40	24

Trace form

\( 144 q + 4 q^{3} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(735, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
735.2.j.a	$735$	$2$	735.j	15.e	$4$	$8$	$4$	$5.869$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(-4\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\zeta_{24}-2\zeta_{24}^{5})q^{2}+(\zeta_{24}+\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
735.2.j.b	$735$	$2$	735.j	15.e	$4$	$8$	$4$	$5.869$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(4\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+2\zeta_{24}^{3}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{4}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
735.2.j.c	$735$	$2$	735.j	15.e	$4$	$16$	$8$	$5.869$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{2}+(\beta _{1}-\beta _{2}-\beta _{8})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
735.2.j.d	$735$	$2$	735.j	15.e	$4$	$16$	$8$	$5.869$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{2}+(-\beta _{6}+\beta _{7}+\beta _{15})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
735.2.j.e	$735$	$2$	735.j	15.e	$4$	$24$	$12$	$5.869$		None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
735.2.j.f	$735$	$2$	735.j	15.e	$4$	$24$	$12$	$5.869$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
735.2.j.g	$735$	$2$	735.j	15.e	$4$	$24$	$12$	$5.869$		None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
735.2.j.h	$735$	$2$	735.j	15.e	$4$	$24$	$12$	$5.869$		None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(735, [\chi])\) into lower level spaces

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