Space of modular forms of level 135, weight 4, and Character 135.e

• Label: 135.4.e
• Level: $135$
• Weight: $4$
• Character orbit: 135.e
• Rep. character: $\chi_{135}(46,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	135.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(135, [\chi])\).

	Total	New	Old
Modular forms	120	24	96
Cusp forms	96	24	72
Eisenstein series	24	0	24

Trace form

24 * q - 4 * q^2 - 48 * q^4 - 10 * q^5 + 12 * q^7 + 108 * q^8 - 46 * q^11 - 24 * q^13 + 6 * q^14 - 192 * q^16 + 500 * q^17 + 300 * q^19 - 120 * q^20 - 36 * q^22 - 192 * q^23 - 300 * q^25 - 1432 * q^26 - 384 * q^28 + 286 * q^29 + 120 * q^31 + 484 * q^32 + 378 * q^34 + 560 * q^35 + 336 * q^37 - 88 * q^38 + 90 * q^40 + 472 * q^41 + 174 * q^43 - 1652 * q^44 + 540 * q^46 - 400 * q^47 - 1026 * q^49 - 100 * q^50 - 1302 * q^52 + 2024 * q^53 + 1530 * q^56 - 594 * q^58 - 298 * q^59 + 858 * q^61 + 1644 * q^62 + 2760 * q^64 - 840 * q^65 + 1362 * q^67 - 2732 * q^68 + 180 * q^70 - 272 * q^71 + 1812 * q^73 + 1480 * q^74 - 2598 * q^76 - 1056 * q^77 - 888 * q^79 + 4560 * q^80 - 3492 * q^82 - 2508 * q^83 - 360 * q^85 + 2762 * q^86 - 432 * q^88 - 7404 * q^89 + 3984 * q^91 - 4140 * q^92 + 1962 * q^94 - 2040 * q^95 - 474 * q^97 - 2696 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(135, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
135.4.e.a	$135$	$4$	135.e	9.c	$3$	$4$	$2$	$7.965$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					45.4.e.a	$2$	$0$	\(-1\)	\(0\)	\(10\)	\(-9\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
135.4.e.b	$135$	$4$	135.e	9.c	$3$	$6$	$3$	$7.965$	6.0.15759792.1	None					45.4.e.b	$2$	$0$	\(-1\)	\(0\)	\(15\)	\(43\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{4})q^{2}+(-\beta _{2}+3\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
135.4.e.c	$135$	$4$	135.e	9.c	$3$	$14$	$7$	$7.965$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None			✓		45.4.e.c	$2$	$0$	\(-2\)	\(0\)	\(-35\)	\(-22\)	$2^{2}\cdot 3^{13}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+(-5-\beta _{3}-5\beta _{5}-\beta _{10}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(135, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(135, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)