Space of modular forms of level 45 and weight 14

• Label: 45.14
• Level: 45
• Weight: 14
• Dimension: 665
• Nonzero newspaces: 6
• Sturm bound: 2016
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(2016\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(45))\).

	Total	New	Old
Modular forms	968	691	277
Cusp forms	904	665	239
Eisenstein series	64	26	38

Trace form

665 * q - 200 * q^2 + 1456 * q^3 + 53970 * q^4 - 1431 * q^5 + 358850 * q^6 + 124852 * q^7 - 691152 * q^8 + 3239924 * q^9 - 2431194 * q^10 - 3367460 * q^11 - 45476560 * q^12 + 36913886 * q^13 + 86538156 * q^14 - 141110564 * q^15 + 3456010 * q^16 + 607911178 * q^17 + 8676016 * q^18 + 31830356 * q^19 - 2777296060 * q^20 + 3149565072 * q^21 + 3352974038 * q^22 - 5759811876 * q^23 - 9343550550 * q^24 - 1982458219 * q^25 + 16483993444 * q^26 - 2365635440 * q^27 - 14408963784 * q^28 - 3735409294 * q^29 + 34755557048 * q^30 + 32549775080 * q^31 - 112739472658 * q^32 - 33833770672 * q^33 + 28193529518 * q^34 + 69831231896 * q^35 + 180657939370 * q^36 - 69098852526 * q^37 - 151865635274 * q^38 - 8034842432 * q^39 - 48544261100 * q^40 + 9106468226 * q^41 + 337880908128 * q^42 + 46989163424 * q^43 - 331191054220 * q^44 - 202256093476 * q^45 - 10571609896 * q^46 + 368988284296 * q^47 + 97304866970 * q^48 - 376582752255 * q^49 - 1440131648930 * q^50 + 247630662632 * q^51 + 2155348046448 * q^52 - 286184233502 * q^53 + 1790812842530 * q^54 - 700930248204 * q^55 - 5438106760020 * q^56 - 2886521767208 * q^57 + 1737944594456 * q^58 + 1988999446732 * q^59 + 1359922344752 * q^60 + 2113271777214 * q^61 + 1776629614236 * q^62 - 1352726678388 * q^63 - 9921734882676 * q^64 + 986863461526 * q^65 + 5901830305924 * q^66 + 7458393806536 * q^67 - 242592068146 * q^68 - 7316929772388 * q^69 - 19616102469126 * q^70 + 2488256691824 * q^71 + 16528657616682 * q^72 + 14915201740694 * q^73 - 187470170476 * q^74 - 20156217216896 * q^75 - 9656541548090 * q^76 - 5794188683580 * q^77 + 5268591328916 * q^78 + 2861505207988 * q^79 + 2027442336152 * q^80 + 2747170660640 * q^81 + 52406516083776 * q^82 - 15800166403920 * q^83 - 12007681666308 * q^84 - 36205481437134 * q^85 - 60068039860802 * q^86 - 3980468008172 * q^87 + 86115776631318 * q^88 + 47927516879250 * q^89 + 2152858145188 * q^90 - 7256775860848 * q^91 - 82931553949764 * q^92 - 56137691129436 * q^93 - 103907636154700 * q^94 + 53505679419736 * q^95 + 110190835459456 * q^96 + 74829576703986 * q^97 + 33945533010158 * q^98 + 28600753076476 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(45))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
45.14.a	\(\chi_{45}(1, \cdot)\)	45.14.a.a	1	1
		45.14.a.b	2
		45.14.a.c	2
		45.14.a.d	2
		45.14.a.e	3
		45.14.a.f	3
		45.14.a.g	4
		45.14.a.h	4
45.14.b	\(\chi_{45}(19, \cdot)\)	45.14.b.a	2	1
		45.14.b.b	6
		45.14.b.c	12
		45.14.b.d	12
45.14.e	\(\chi_{45}(16, \cdot)\)	n/a	104	2
45.14.f	\(\chi_{45}(8, \cdot)\)	45.14.f.a	52	2
45.14.j	\(\chi_{45}(4, \cdot)\)	n/a	152	2
45.14.l	\(\chi_{45}(2, \cdot)\)	n/a	304	4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)