Space of modular forms of level 105 and weight 8

• Label: 105.8
• Level: 105
• Weight: 8
• Dimension: 1740
• Nonzero newspaces: 12
• Sturm bound: 6144
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(6144\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(105))\).

	Total	New	Old
Modular forms	2784	1796	988
Cusp forms	2592	1740	852
Eisenstein series	192	56	136

Trace form

1740 * q + 56 * q^2 - 108 * q^3 - 636 * q^4 + 882 * q^5 - 144 * q^6 - 2292 * q^7 - 2436 * q^8 + 8892 * q^9 - 8960 * q^10 - 10900 * q^11 + 25596 * q^12 + 5692 * q^13 + 113064 * q^14 - 69564 * q^15 - 268468 * q^16 - 59944 * q^17 + 203280 * q^18 + 180044 * q^19 + 369748 * q^20 - 93048 * q^21 - 1234080 * q^22 - 977280 * q^23 + 795636 * q^24 + 253404 * q^25 + 1030700 * q^26 + 180708 * q^27 + 1838044 * q^28 - 482984 * q^29 - 125802 * q^30 - 1616908 * q^31 - 829124 * q^32 - 1247724 * q^33 - 3086920 * q^34 - 1913122 * q^35 - 784260 * q^36 + 4973712 * q^37 + 6147428 * q^38 + 2756364 * q^39 + 11338448 * q^40 - 1766480 * q^41 - 9271368 * q^42 - 8922048 * q^43 - 4299104 * q^44 - 2205714 * q^45 - 3596488 * q^46 - 398068 * q^47 + 5925900 * q^48 - 3250320 * q^49 + 13106900 * q^50 - 2988864 * q^51 + 8306296 * q^52 + 75536 * q^53 + 14275104 * q^54 + 4518432 * q^55 - 11610372 * q^56 - 8040048 * q^57 - 8532072 * q^58 - 901864 * q^59 - 10205784 * q^60 - 12647308 * q^61 - 6481872 * q^62 - 14987328 * q^63 - 13505452 * q^64 + 15454454 * q^65 + 69595236 * q^66 + 55477940 * q^67 - 12250472 * q^68 - 3986496 * q^69 - 79792920 * q^70 - 34371128 * q^71 - 87478152 * q^72 - 18828848 * q^73 - 14778596 * q^74 + 3652080 * q^75 + 55574848 * q^76 + 66916272 * q^77 + 94473144 * q^78 + 73887564 * q^79 + 48209032 * q^80 + 11726040 * q^81 - 21206520 * q^82 - 6744024 * q^83 - 93946788 * q^84 + 9631336 * q^85 - 19952428 * q^86 - 101822592 * q^87 - 184670592 * q^88 - 108754920 * q^89 - 59638716 * q^90 - 41340464 * q^91 - 15191040 * q^92 + 144548712 * q^93 + 231688424 * q^94 + 119369078 * q^95 + 206925024 * q^96 + 196565896 * q^97 + 129770788 * q^98 - 33422016 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(105))\)

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
105.8.a	\(\chi_{105}(1, \cdot)\)	105.8.a.a	1	1
		105.8.a.b	1
		105.8.a.c	2
		105.8.a.d	4
		105.8.a.e	4
		105.8.a.f	4
		105.8.a.g	4
		105.8.a.h	4
		105.8.a.i	4
105.8.b	\(\chi_{105}(41, \cdot)\)	105.8.b.a	38	1
		105.8.b.b	38
105.8.d	\(\chi_{105}(64, \cdot)\)	105.8.d.a	18	1
		105.8.d.b	22
105.8.g	\(\chi_{105}(104, \cdot)\)	n/a	108	1
105.8.i	\(\chi_{105}(16, \cdot)\)	105.8.i.a	18	2
		105.8.i.b	18
		105.8.i.c	20
		105.8.i.d	20
105.8.j	\(\chi_{105}(8, \cdot)\)	n/a	168	2
105.8.m	\(\chi_{105}(13, \cdot)\)	n/a	112	2
105.8.p	\(\chi_{105}(59, \cdot)\)	n/a	216	2
105.8.q	\(\chi_{105}(4, \cdot)\)	n/a	112	2
105.8.s	\(\chi_{105}(26, \cdot)\)	n/a	148	2
105.8.u	\(\chi_{105}(52, \cdot)\)	n/a	224	4
105.8.x	\(\chi_{105}(2, \cdot)\)	n/a	432	4

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(105))\) into lower level spaces

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