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

• Label: 675.2.u
• Level: $675$
• Weight: $2$
• Character orbit: 675.u
• Rep. character: $\chi_{675}(49,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $312$
• Newform subspaces: $5$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$675 = 3^{3} \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	675.u (of order $18$ and degree $6$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$135$
Character field:			$\Q(\zeta_{18})$
Newform subspaces:			$5$
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	576	336	240
Cusp forms	504	312	192
Eisenstein series	72	24	48

Trace form

312 * q + 12 * q^4 - 24 * q^6 + 24 * q^9 - 24 * q^11 + 24 * q^14 + 6 * q^19 - 48 * q^21 - 6 * q^24 - 96 * q^26 + 48 * q^29 + 6 * q^31 - 96 * q^36 + 30 * q^39 - 12 * q^41 - 102 * q^44 - 6 * q^46 + 48 * q^49 - 54 * q^51 - 192 * q^54 + 138 * q^56 + 42 * q^59 - 48 * q^61 + 120 * q^64 + 174 * q^66 - 60 * q^69 + 78 * q^71 - 138 * q^74 + 12 * q^76 - 60 * q^79 - 186 * q^84 - 42 * q^86 - 36 * q^89 - 6 * q^91 - 60 * q^94 - 168 * q^96 - 24 * q^99

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.u.a	$675$	$2$	675.u	135.p	$18$	$12$	$2$	$5.390$	$\Q(\zeta_{36})$	None		✓			675.2.l.a	$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{18}]$	$q+(-\zeta_{36}^{5}+\zeta_{36}^{7}-\zeta_{36}^{9})q^{2}+(-2\zeta_{36}^{5}+\cdots)q^{3}+\cdots$
675.2.u.b	$675$	$2$	675.u	135.p	$18$	$24$	$4$	$5.390$		None					27.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{18}]$
675.2.u.c	$675$	$2$	675.u	135.p	$18$	$60$	$10$	$5.390$		None					135.2.k.a	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{18}]$
675.2.u.d	$675$	$2$	675.u	135.p	$18$	$84$	$14$	$5.390$		None					135.2.k.b	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{18}]$
675.2.u.e	$675$	$2$	675.u	135.p	$18$	$132$	$22$	$5.390$		None		✓	✓		675.2.l.f	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{18}]$

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

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