Space of modular forms of level 135, weight 2, and Character 135.f

• Label: 135.2.f
• Level: $135$
• Weight: $2$
• Character orbit: 135.f
• Rep. character: $\chi_{135}(53,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $7$

Defining parameters

Level:	$N$	$=$	$135 = 3^{3} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	135.f (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$15$
Character field:			$\Q(i)$
Newform subspaces:			$2$
Sturm bound:			$36$
Trace bound:			$7$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(135, [\chi])$.

	Total	New	Old
Modular forms	48	16	32
Cusp forms	24	16	8
Eisenstein series	24	0	24

Trace form

16 * q + 4 * q^7 + 4 * q^10 - 20 * q^13 - 20 * q^16 - 4 * q^22 - 8 * q^25 - 4 * q^28 + 8 * q^31 - 56 * q^37 + 60 * q^40 + 52 * q^43 - 28 * q^46 + 52 * q^52 - 4 * q^55 - 24 * q^58 - 16 * q^61 - 8 * q^67 - 120 * q^70 - 20 * q^73 + 36 * q^76 + 92 * q^82 - 20 * q^85 + 84 * q^88 + 80 * q^91 + 40 * q^97

Decomposition of $S_{2}^{\mathrm{new}}(135, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
135.2.f.a	$135$	$2$	135.f	15.e	$4$	$8$	$4$	$1.078$	8.0.$\cdots$.1	None		✓			135.2.f.a	$4$	$0$	$0$	$0$	$0$	$-4$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(-\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots$
135.2.f.b	$135$	$2$	135.f	15.e	$4$	$8$	$4$	$1.078$	8.0.$\cdots$.8	None		✓			135.2.f.b	$4$	$0$	$0$	$0$	$0$	$8$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(2\beta _{2}+\beta _{3}+\beta _{6})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(135, [\chi])$ into lower level spaces

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