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

• Label: 135.2.e
• Level: $135$
• Weight: $2$
• Character orbit: 135.e
• Rep. character: $\chi_{135}(46,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$135 = 3^{3} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	135.e (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$9$
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$2$
Sturm bound:			$36$
Trace bound:			$1$
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	8	40
Cusp forms	24	8	16
Eisenstein series	24	0	24

Trace form

8 * q + 2 * q^2 - 4 * q^4 + 2 * q^5 - 2 * q^7 - 4 * q^11 - 2 * q^13 - 12 * q^14 - 4 * q^16 - 4 * q^17 - 8 * q^19 + 6 * q^20 + 6 * q^22 + 6 * q^23 - 4 * q^25 + 8 * q^26 + 16 * q^28 - 8 * q^29 - 8 * q^31 + 22 * q^32 - 16 * q^35 + 4 * q^37 - 10 * q^38 - 6 * q^40 - 8 * q^41 - 2 * q^43 + 40 * q^44 + 20 * q^47 + 2 * q^50 + 10 * q^52 + 8 * q^53 + 18 * q^58 - 16 * q^59 - 8 * q^61 - 84 * q^62 - 16 * q^64 + 6 * q^65 - 8 * q^67 - 26 * q^68 + 6 * q^70 + 16 * q^71 - 8 * q^73 - 20 * q^74 + 4 * q^76 + 6 * q^77 + 4 * q^79 - 12 * q^80 - 48 * q^82 - 6 * q^83 + 6 * q^85 + 20 * q^86 + 18 * q^88 + 48 * q^89 + 32 * q^91 + 36 * q^92 + 24 * q^94 + 12 * q^95 + 16 * q^97 + 76 * q^98

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.e.a	$135$	$2$	135.e	9.c	$3$	$2$	$1$	$1.078$	$\Q(\sqrt{-3})$	None					45.2.e.a	$2$	$0$	$1$	$0$	$-1$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots$
135.2.e.b	$135$	$2$	135.e	9.c	$3$	$6$	$3$	$1.078$	6.0.954288.1	None			✓		45.2.e.b	$2$	$0$	$1$	$0$	$3$	$-5$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$

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}$