Space of modular forms of level 45, weight 6, and Character 45.j

• Label: 45.6.j
• Level: $45$
• Weight: $6$
• Character orbit: 45.j
• Rep. character: $\chi_{45}(4,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$45 = 3^{2} \cdot 5$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	45.j (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$45$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$1$
Sturm bound:			$36$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{6}(45, [\chi])$.

	Total	New	Old
Modular forms	64	64	0
Cusp forms	56	56	0
Eisenstein series	8	8	0

Trace form

56 * q + 414 * q^4 - 30 * q^5 + 12 * q^6 + 468 * q^9 - 68 * q^10 - 780 * q^11 + 1398 * q^14 + 672 * q^15 - 5570 * q^16 - 8 * q^19 + 3522 * q^20 - 4848 * q^21 - 7554 * q^24 - 1654 * q^25 + 16968 * q^26 + 2700 * q^29 + 22578 * q^30 - 4436 * q^31 - 6268 * q^34 - 16344 * q^35 + 38016 * q^36 + 2508 * q^39 + 2036 * q^40 - 38928 * q^41 - 119400 * q^44 - 55890 * q^45 + 45764 * q^46 + 40244 * q^49 - 26466 * q^50 - 2964 * q^51 + 132894 * q^54 + 21024 * q^55 - 59442 * q^56 + 70200 * q^59 + 165084 * q^60 + 23368 * q^61 - 164668 * q^64 - 39210 * q^65 + 49452 * q^66 - 167076 * q^69 + 49752 * q^70 + 175176 * q^71 + 180168 * q^74 - 33528 * q^75 - 27348 * q^76 - 53480 * q^79 + 485892 * q^80 - 365112 * q^81 - 334242 * q^84 + 43936 * q^85 - 18060 * q^86 - 685536 * q^89 - 378936 * q^90 - 99576 * q^91 + 9614 * q^94 - 380028 * q^95 - 798 * q^96 + 1001340 * q^99

Decomposition of $S_{6}^{\mathrm{new}}(45, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.6.j.a	$45$	$6$	45.j	45.j	$6$	$56$	$28$	$7.217$		None		✓	✓	✓	45.6.j.a	$4$	$0$	$0$	$0$	$-30$	$0$		$\mathrm{SU}(2)[C_{6}]$