Space of modular forms of level 105 and weight 4

• Label: 105.4
• Level: 105
• Weight: 4
• Dimension: 728
• Nonzero newspaces: 12
• Newform subspaces: 27
• Sturm bound: 3072
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 27 \)
Sturm bound:			\(3072\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(105))\).

	Total	New	Old
Modular forms	1248	784	464
Cusp forms	1056	728	328
Eisenstein series	192	56	136

Trace form

728 * q - 8 * q^2 - 6 * q^3 + 36 * q^4 + 12 * q^5 + 48 * q^6 + 104 * q^7 - 36 * q^8 - 54 * q^9 + 120 * q^10 + 112 * q^11 - 36 * q^12 - 184 * q^13 + 360 * q^14 - 174 * q^15 - 404 * q^16 - 56 * q^17 - 144 * q^18 - 628 * q^19 - 172 * q^20 - 606 * q^21 + 128 * q^22 + 912 * q^23 + 1044 * q^24 + 1574 * q^25 + 1948 * q^26 - 408 * q^27 + 2268 * q^28 - 472 * q^29 - 1722 * q^30 - 868 * q^31 - 1828 * q^32 - 306 * q^33 - 1576 * q^34 - 2012 * q^35 - 2244 * q^36 - 2364 * q^37 - 4748 * q^38 - 2028 * q^39 - 1712 * q^40 + 728 * q^41 - 3360 * q^42 - 1432 * q^43 - 448 * q^44 + 321 * q^45 + 2456 * q^46 + 880 * q^47 + 6252 * q^48 + 3832 * q^49 + 3700 * q^50 + 7002 * q^51 + 10584 * q^52 + 3976 * q^53 + 8736 * q^54 + 7812 * q^55 + 9468 * q^56 + 2460 * q^57 + 4904 * q^58 + 3616 * q^59 - 1704 * q^60 - 8124 * q^61 - 7056 * q^62 - 6618 * q^63 - 22284 * q^64 - 8936 * q^65 - 12588 * q^66 - 14204 * q^67 - 14920 * q^68 - 3600 * q^69 - 19800 * q^70 - 4072 * q^71 + 7896 * q^72 + 3644 * q^73 - 724 * q^74 + 6645 * q^75 + 11104 * q^76 + 216 * q^77 + 1320 * q^78 + 8068 * q^79 + 3752 * q^80 - 9546 * q^81 - 1944 * q^82 - 288 * q^83 - 7476 * q^84 + 3516 * q^85 + 388 * q^86 - 3396 * q^87 + 11520 * q^88 + 5256 * q^89 - 9876 * q^90 - 3248 * q^91 + 7296 * q^92 - 4986 * q^93 - 7864 * q^94 - 7952 * q^95 + 4896 * q^96 - 5592 * q^97 + 12932 * q^98 + 13956 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(105))\)

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
105.4.a	\(\chi_{105}(1, \cdot)\)	105.4.a.a	1	1
		105.4.a.b	1
		105.4.a.c	2
		105.4.a.d	2
		105.4.a.e	2
		105.4.a.f	2
		105.4.a.g	2
105.4.b	\(\chi_{105}(41, \cdot)\)	105.4.b.a	16	1
		105.4.b.b	16
105.4.d	\(\chi_{105}(64, \cdot)\)	105.4.d.a	6	1
		105.4.d.b	10
105.4.g	\(\chi_{105}(104, \cdot)\)	105.4.g.a	4	1
		105.4.g.b	40
105.4.i	\(\chi_{105}(16, \cdot)\)	105.4.i.a	2	2
		105.4.i.b	4
		105.4.i.c	6
		105.4.i.d	10
		105.4.i.e	10
105.4.j	\(\chi_{105}(8, \cdot)\)	105.4.j.a	72	2
105.4.m	\(\chi_{105}(13, \cdot)\)	105.4.m.a	48	2
105.4.p	\(\chi_{105}(59, \cdot)\)	105.4.p.a	88	2
105.4.q	\(\chi_{105}(4, \cdot)\)	105.4.q.a	4	2
		105.4.q.b	44
105.4.s	\(\chi_{105}(26, \cdot)\)	105.4.s.a	32	2
		105.4.s.b	32
105.4.u	\(\chi_{105}(52, \cdot)\)	105.4.u.a	96	4
105.4.x	\(\chi_{105}(2, \cdot)\)	105.4.x.a	176	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(105))\) into lower level spaces

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