Space of modular forms of level 45, weight 10, and Character 45.e

• Label: 45.10.e
• Level: $45$
• Weight: $10$
• Character orbit: 45.e
• Rep. character: $\chi_{45}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(60\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(45, [\chi])\).

	Total	New	Old
Modular forms	112	72	40
Cusp forms	104	72	32
Eisenstein series	8	0	8

Trace form

72 * q - 32 * q^2 - 146 * q^3 - 9216 * q^4 - 1250 * q^5 + 686 * q^6 + 684 * q^7 + 30996 * q^8 + 26408 * q^9 - 65762 * q^11 + 371258 * q^12 - 64872 * q^13 - 416562 * q^14 - 132500 * q^15 - 2359296 * q^16 + 609700 * q^17 + 364720 * q^18 + 341100 * q^19 - 960000 * q^20 - 1489320 * q^21 - 1056672 * q^22 - 5057664 * q^23 + 6269484 * q^24 - 14062500 * q^25 - 22712264 * q^26 + 15967708 * q^27 - 1400832 * q^28 + 3730718 * q^29 - 3910000 * q^30 + 7808760 * q^31 + 4220012 * q^32 + 25209614 * q^33 + 3797766 * q^34 + 24010000 * q^35 + 99710434 * q^36 - 12953808 * q^37 - 34904036 * q^38 - 85429040 * q^39 + 14546250 * q^40 - 57017056 * q^41 - 63196410 * q^42 - 30499218 * q^43 + 335994404 * q^44 + 37617500 * q^45 - 2389500 * q^46 - 212892800 * q^47 - 407302684 * q^48 - 229999662 * q^49 - 12500000 * q^50 - 16382782 * q^51 + 40594266 * q^52 + 396712648 * q^53 + 463138364 * q^54 - 701221770 * q^56 - 803169578 * q^57 - 213788322 * q^58 - 192564854 * q^59 + 52786250 * q^60 - 150612066 * q^61 + 1720996932 * q^62 + 760620384 * q^63 + 1845389160 * q^64 - 165885000 * q^65 - 2209090772 * q^66 + 49500594 * q^67 - 676640524 * q^68 + 1052381202 * q^69 + 156060000 * q^70 + 816701456 * q^71 + 3029937480 * q^72 - 1197226404 * q^73 - 101741440 * q^74 - 57031250 * q^75 - 157113774 * q^76 - 1967703648 * q^77 - 1256901814 * q^78 + 83541384 * q^79 + 2217270000 * q^80 + 533909468 * q^81 - 782513244 * q^82 - 1450533396 * q^83 + 2593756734 * q^84 - 255015000 * q^85 - 902718566 * q^86 - 1733776040 * q^87 - 811524096 * q^88 + 1651061508 * q^89 + 1248561250 * q^90 + 780527952 * q^91 - 2556692820 * q^92 + 1474457352 * q^93 + 2170806534 * q^94 - 1327845000 * q^95 - 5488203302 * q^96 - 304374798 * q^97 - 6759724432 * q^98 - 4901925284 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.10.e.a	$45$	$10$	45.e	9.c	$3$	$34$	$17$	$23.177$		None		✓			45.10.e.a	$2$	$0$	\(-16\)	\(-285\)	\(10625\)	\(9946\)		$\mathrm{SU}(2)[C_{3}]$
45.10.e.b	$45$	$10$	45.e	9.c	$3$	$38$	$19$	$23.177$		None		✓	✓		45.10.e.b	$2$	$0$	\(-16\)	\(139\)	\(-11875\)	\(-9262\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{10}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)