Space of modular forms of level 105 and weight 5

• Label: 105.5
• Level: 105
• Weight: 5
• Dimension: 980
• Nonzero newspaces: 12
• Newform subspaces: 15
• Sturm bound: 3840
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 15 \)
Sturm bound:			\(3840\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(105))\).

	Total	New	Old
Modular forms	1632	1044	588
Cusp forms	1440	980	460
Eisenstein series	192	64	128

Trace form

980 * q - 4 * q^3 - 124 * q^4 + 114 * q^5 + 52 * q^6 + 100 * q^7 + 756 * q^8 - 320 * q^9 - 188 * q^10 - 468 * q^11 + 256 * q^12 + 884 * q^13 + 1296 * q^14 - 772 * q^15 + 12 * q^16 - 72 * q^17 + 860 * q^18 + 2580 * q^19 - 1128 * q^20 - 3972 * q^21 - 8200 * q^22 - 2640 * q^23 - 2352 * q^24 - 2584 * q^25 + 684 * q^26 + 704 * q^27 + 11212 * q^28 + 9144 * q^29 + 9892 * q^30 + 16452 * q^31 + 10380 * q^32 - 5432 * q^33 - 14432 * q^34 - 9174 * q^35 + 11300 * q^36 - 5312 * q^37 - 8220 * q^38 + 9548 * q^39 - 6360 * q^40 - 5664 * q^41 - 1020 * q^42 + 15768 * q^43 + 2448 * q^44 - 11516 * q^45 - 33896 * q^46 - 17412 * q^47 - 76016 * q^48 - 45368 * q^49 - 2772 * q^50 - 10796 * q^51 - 16440 * q^52 - 7008 * q^53 + 66700 * q^54 + 5748 * q^55 + 32124 * q^56 + 60152 * q^57 + 100760 * q^58 + 47016 * q^59 + 22840 * q^60 + 55876 * q^61 + 56040 * q^62 + 22740 * q^63 + 40852 * q^64 + 60690 * q^65 - 24328 * q^66 - 31092 * q^67 - 45552 * q^68 - 94608 * q^69 - 113100 * q^70 - 100176 * q^71 - 71832 * q^72 - 89296 * q^73 - 53532 * q^74 - 26878 * q^75 - 40040 * q^76 - 38952 * q^77 + 83656 * q^78 + 11284 * q^79 - 45552 * q^80 + 101044 * q^81 + 139440 * q^82 + 105120 * q^83 + 64728 * q^84 + 138760 * q^85 + 41052 * q^86 - 25696 * q^87 - 85176 * q^88 - 49464 * q^89 - 64360 * q^90 - 46952 * q^91 - 59880 * q^92 - 120660 * q^93 - 36800 * q^94 - 17262 * q^95 - 90052 * q^96 - 61248 * q^97 + 7524 * q^98 - 13648 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(105))\)

We only show spaces with odd 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
105.5.c	\(\chi_{105}(71, \cdot)\)	105.5.c.a	32	1
105.5.e	\(\chi_{105}(34, \cdot)\)	105.5.e.a	32	1
105.5.f	\(\chi_{105}(29, \cdot)\)	105.5.f.a	48	1
105.5.h	\(\chi_{105}(76, \cdot)\)	105.5.h.a	20	1
105.5.k	\(\chi_{105}(62, \cdot)\)	105.5.k.a	120	2
105.5.l	\(\chi_{105}(22, \cdot)\)	105.5.l.a	48	2
105.5.n	\(\chi_{105}(31, \cdot)\)	105.5.n.a	4	2
		105.5.n.b	8
		105.5.n.c	12
		105.5.n.d	20
105.5.o	\(\chi_{105}(44, \cdot)\)	105.5.o.a	120	2
105.5.r	\(\chi_{105}(19, \cdot)\)	105.5.r.a	64	2
105.5.t	\(\chi_{105}(11, \cdot)\)	105.5.t.a	84	2
105.5.v	\(\chi_{105}(37, \cdot)\)	105.5.v.a	128	4
105.5.w	\(\chi_{105}(17, \cdot)\)	105.5.w.a	240	4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(105))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(105)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)