Space of modular forms of level 45 and weight 10

• Label: 45.10
• Level: 45
• Weight: 10
• Dimension: 457
• Nonzero newspaces: 6
• Newform subspaces: 17
• Sturm bound: 1440
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1440\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(45))\).

	Total	New	Old
Modular forms	680	483	197
Cusp forms	616	457	159
Eisenstein series	64	26	38

Trace form

457 * q - 88 * q^2 - 2 * q^3 + 2642 * q^4 - 1536 * q^5 - 4894 * q^6 + 22488 * q^7 - 24336 * q^8 - 8926 * q^9 + 113846 * q^10 - 188644 * q^11 + 179312 * q^12 + 82664 * q^13 + 192012 * q^14 - 482099 * q^15 + 577290 * q^16 + 122558 * q^17 + 1528336 * q^18 + 677272 * q^19 + 3650500 * q^20 - 2080002 * q^21 - 1577450 * q^22 + 1837152 * q^23 + 7579914 * q^24 - 17386994 * q^25 - 16093564 * q^26 + 10126816 * q^27 + 24461848 * q^28 + 29665264 * q^29 - 8581912 * q^30 - 26040998 * q^31 - 59931602 * q^32 - 6375568 * q^33 - 21044242 * q^34 + 39110416 * q^35 + 45514666 * q^36 + 76226434 * q^37 - 24517450 * q^38 - 93468662 * q^39 - 217671420 * q^40 - 149667386 * q^41 - 45485664 * q^42 + 146578886 * q^43 + 529176820 * q^44 + 18901019 * q^45 + 155799704 * q^46 - 465144928 * q^47 - 331251814 * q^48 - 212728589 * q^49 + 406863470 * q^50 + 174938414 * q^51 + 563961808 * q^52 + 510071426 * q^53 + 212209922 * q^54 - 305009574 * q^55 - 851713812 * q^56 - 479228714 * q^57 - 195878888 * q^58 - 58219012 * q^59 + 639842432 * q^60 + 213848016 * q^61 + 1421788764 * q^62 + 1229848410 * q^63 + 872981388 * q^64 - 1274140249 * q^65 - 4669726268 * q^66 - 1699199934 * q^67 - 2746582802 * q^68 + 1846341378 * q^69 + 1561139034 * q^70 + 3521854804 * q^71 + 3121962858 * q^72 - 1669881346 * q^73 + 1339446676 * q^74 + 819681409 * q^75 + 1990291206 * q^76 - 3038288262 * q^77 - 5941861036 * q^78 + 1039418174 * q^79 - 1076637608 * q^80 + 2083342130 * q^81 - 3862183488 * q^82 - 926051112 * q^83 + 4830712476 * q^84 + 1571050376 * q^85 + 3487645214 * q^86 - 3635090618 * q^87 - 1176819690 * q^88 - 320139066 * q^89 - 9438177692 * q^90 + 2860132416 * q^91 + 6132351516 * q^92 + 6817923414 * q^93 + 3806416532 * q^94 + 2049376916 * q^95 + 5158612576 * q^96 - 11019950462 * q^97 - 12074509538 * q^98 - 4109380118 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.10.a	\(\chi_{45}(1, \cdot)\)	45.10.a.a	1	1
		45.10.a.b	1
		45.10.a.c	1
		45.10.a.d	2
		45.10.a.e	2
		45.10.a.f	2
		45.10.a.g	3
		45.10.a.h	3
45.10.b	\(\chi_{45}(19, \cdot)\)	45.10.b.a	2	1
		45.10.b.b	4
		45.10.b.c	8
		45.10.b.d	8
45.10.e	\(\chi_{45}(16, \cdot)\)	45.10.e.a	34	2
		45.10.e.b	38
45.10.f	\(\chi_{45}(8, \cdot)\)	45.10.f.a	36	2
45.10.j	\(\chi_{45}(4, \cdot)\)	45.10.j.a	104	2
45.10.l	\(\chi_{45}(2, \cdot)\)	45.10.l.a	208	4

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)