Space of modular forms of level 45, weight 12, and Character 45.e

• Label: 45.12.e
• Level: $45$
• Weight: $12$
• Character orbit: 45.e
• Rep. character: $\chi_{45}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $88$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(45, [\chi])\).

	Total	New	Old
Modular forms	136	88	48
Cusp forms	128	88	40
Eisenstein series	8	0	8

Trace form

88 * q + 64 * q^2 + 526 * q^3 - 45056 * q^4 + 6250 * q^5 - 40018 * q^6 - 17026 * q^7 + 66420 * q^8 - 273988 * q^9 - 905780 * q^11 + 375242 * q^12 - 559414 * q^13 + 2265438 * q^14 + 268750 * q^15 - 46137344 * q^16 - 44954708 * q^17 - 13952960 * q^18 - 14058808 * q^19 + 19200000 * q^20 - 30400200 * q^21 - 4540992 * q^22 + 115321818 * q^23 + 286991532 * q^24 - 429687500 * q^25 - 481821704 * q^26 - 57262106 * q^27 + 139476992 * q^28 - 33603376 * q^29 - 91450000 * q^30 - 152541832 * q^31 - 852721876 * q^32 + 114734420 * q^33 + 327302262 * q^34 - 840350000 * q^35 - 787778654 * q^36 - 642873268 * q^37 + 2817916060 * q^38 + 2599065340 * q^39 - 160443750 * q^40 - 2458361536 * q^41 - 2988938826 * q^42 + 2237695166 * q^43 + 2323962788 * q^44 + 2882525000 * q^45 - 2882533500 * q^46 + 3689828380 * q^47 + 6584119460 * q^48 - 9348573744 * q^49 + 625000000 * q^50 + 593461640 * q^51 - 7248124630 * q^52 - 18439902296 * q^53 - 12051224596 * q^54 + 29605877190 * q^56 + 4795420066 * q^57 + 10743544926 * q^58 + 22788803848 * q^59 - 9136393750 * q^60 + 3522836600 * q^61 - 119653567548 * q^62 - 60179357832 * q^63 + 114160686664 * q^64 + 3991743750 * q^65 + 54523237132 * q^66 - 23577765664 * q^67 + 42904312292 * q^68 - 24531097608 * q^69 - 9094200000 * q^70 - 139459703056 * q^71 - 244408755192 * q^72 + 25225787864 * q^73 + 128680773920 * q^74 + 5136718750 * q^75 - 6652521646 * q^76 + 146729573022 * q^77 - 102122550646 * q^78 - 12509227228 * q^79 - 97067850000 * q^80 - 133287853108 * q^81 + 180332440356 * q^82 + 22202116062 * q^83 + 642140256702 * q^84 + 27456431250 * q^85 + 264797663242 * q^86 - 259808887658 * q^87 - 13949927424 * q^88 - 217231479552 * q^89 - 217241918750 * q^90 - 224401067936 * q^91 + 760554415692 * q^92 + 469862368146 * q^93 + 94560174102 * q^94 + 170951212500 * q^95 - 337687009574 * q^96 - 176645136472 * q^97 - 1460568029872 * q^98 - 317921493632 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.12.e.a	$45$	$12$	45.e	9.c	$3$	$42$	$21$	$34.575$		None		✓			45.12.e.a	$2$	$0$	\(32\)	\(177\)	\(-65625\)	\(58715\)		$\mathrm{SU}(2)[C_{3}]$
45.12.e.b	$45$	$12$	45.e	9.c	$3$	$46$	$23$	$34.575$		None		✓	✓		45.12.e.b	$2$	$0$	\(32\)	\(349\)	\(71875\)	\(-75741\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{12}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)