Space of modular forms of level 45, weight 8, and Character 45.e

• Label: 45.8.e
• Level: $45$
• Weight: $8$
• Character orbit: 45.e
• Rep. character: $\chi_{45}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(45, [\chi])\).

	Total	New	Old
Modular forms	88	56	32
Cusp forms	80	56	24
Eisenstein series	8	0	8

Trace form

56 * q + 16 * q^2 - 26 * q^3 - 1792 * q^4 + 250 * q^5 + 1790 * q^6 + 166 * q^7 - 11340 * q^8 - 3748 * q^9 + 3316 * q^11 - 4822 * q^12 + 3694 * q^13 + 20046 * q^14 + 1750 * q^15 - 114688 * q^16 - 6692 * q^17 + 76480 * q^18 - 48872 * q^19 + 48000 * q^20 + 250560 * q^21 + 70512 * q^22 + 192882 * q^23 - 216660 * q^24 - 437500 * q^25 - 504584 * q^26 - 277994 * q^27 - 84992 * q^28 + 298340 * q^29 + 452000 * q^30 - 215048 * q^31 + 1859756 * q^32 - 70600 * q^33 + 17766 * q^34 - 686000 * q^35 - 2547038 * q^36 + 24868 * q^37 + 1305100 * q^38 + 1161100 * q^39 - 399750 * q^40 + 2099384 * q^41 - 1647114 * q^42 - 816746 * q^43 - 3551836 * q^44 - 1864000 * q^45 + 1684260 * q^46 + 3949180 * q^47 + 6612260 * q^48 - 3261492 * q^49 + 250000 * q^50 - 3937504 * q^51 - 1297910 * q^52 + 409096 * q^53 - 2048692 * q^54 - 115290 * q^56 + 10448314 * q^57 + 2589534 * q^58 - 4589840 * q^59 - 1681750 * q^60 + 4157908 * q^61 - 9876732 * q^62 + 10453272 * q^63 + 1765256 * q^64 + 2930250 * q^65 - 7041236 * q^66 - 4672856 * q^67 + 857348 * q^68 + 1406244 * q^69 + 582000 * q^70 + 5301488 * q^71 - 14957688 * q^72 + 21340096 * q^73 - 15530560 * q^74 - 406250 * q^75 + 9772498 * q^76 + 4305738 * q^77 - 50134 * q^78 - 5687180 * q^79 - 2634000 * q^80 + 27011564 * q^81 + 225924 * q^82 - 11334162 * q^83 - 59869890 * q^84 + 1317750 * q^85 - 43238054 * q^86 - 5487842 * q^87 + 13538304 * q^88 + 43184616 * q^89 + 6129250 * q^90 - 15371200 * q^91 - 41793012 * q^92 - 23461386 * q^93 - 14211930 * q^94 + 8398500 * q^95 + 24357850 * q^96 + 9274252 * q^97 + 62594672 * q^98 + 57087520 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.8.e.a	$45$	$8$	45.e	9.c	$3$	$26$	$13$	$14.057$		None		✓			45.8.e.a	$2$	$0$	\(8\)	\(-27\)	\(-1625\)	\(1455\)		$\mathrm{SU}(2)[C_{3}]$
45.8.e.b	$45$	$8$	45.e	9.c	$3$	$30$	$15$	$14.057$		None		✓	✓		45.8.e.b	$2$	$0$	\(8\)	\(1\)	\(1875\)	\(-1289\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{8}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)