Space of modular forms of level 675, weight 2, and Character 675.k

• Label: 675.2.k
• Level: $675$
• Weight: $2$
• Character orbit: 675.k
• Rep. character: $\chi_{675}(199,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(675, [\chi])\).

	Total	New	Old
Modular forms	216	40	176
Cusp forms	144	32	112
Eisenstein series	72	8	64

Trace form

\( 32 q + 16 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(675, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
675.2.k.a	$675$	$2$	675.k	45.j	$6$	$4$	$2$	$5.390$	\(\Q(\zeta_{12})\)	None					45.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{4}+3\zeta_{12}q^{7}-3\zeta_{12}^{3}q^{8}+\cdots\)
675.2.k.b	$675$	$2$	675.k	45.j	$6$	$12$	$6$	$5.390$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					45.2.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{8}q^{2}+(2\beta _{6}-\beta _{9})q^{4}+(-\beta _{3}+\beta _{7}+\cdots)q^{7}+\cdots\)
675.2.k.c	$675$	$2$	675.k	45.j	$6$	$16$	$8$	$5.390$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		225.2.e.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(1+\beta _{3}+\beta _{7}+\beta _{11})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(675, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)