Space of modular forms of level 104 and weight 4

• Label: 104.4
• Level: 104
• Weight: 4
• Dimension: 537
• Nonzero newspaces: 10
• Newform subspaces: 17
• Sturm bound: 2688
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(2688\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(104))\).

	Total	New	Old
Modular forms	1080	581	499
Cusp forms	936	537	399
Eisenstein series	144	44	100

Trace form

537 * q - 8 * q^2 - 4 * q^3 + 12 * q^4 + 4 * q^5 - 68 * q^6 - 28 * q^7 - 92 * q^8 + 2 * q^9 + 100 * q^10 + 76 * q^11 + 100 * q^12 - 22 * q^13 - 56 * q^14 - 252 * q^15 - 44 * q^16 - 209 * q^17 - 16 * q^18 - 304 * q^19 - 236 * q^20 + 312 * q^21 + 156 * q^22 + 936 * q^23 + 212 * q^24 + 541 * q^25 - 292 * q^26 + 500 * q^27 - 204 * q^28 - 201 * q^29 + 212 * q^30 - 648 * q^31 + 692 * q^32 - 1456 * q^33 - 68 * q^34 - 696 * q^35 + 288 * q^36 + 3 * q^37 + 380 * q^38 + 1896 * q^39 + 3416 * q^40 + 1183 * q^41 + 3244 * q^42 + 892 * q^43 - 48 * q^44 - 449 * q^45 - 3140 * q^46 - 3528 * q^47 - 5100 * q^48 + 86 * q^49 - 5252 * q^50 - 3272 * q^51 - 4960 * q^52 - 1280 * q^53 - 6328 * q^54 - 2324 * q^55 - 2720 * q^56 - 708 * q^57 + 804 * q^58 + 1504 * q^59 + 3852 * q^60 + 655 * q^61 + 4424 * q^62 + 1180 * q^63 + 6396 * q^64 - 2765 * q^65 + 7944 * q^66 + 1088 * q^67 - 348 * q^68 - 268 * q^69 + 592 * q^70 + 500 * q^71 + 68 * q^72 + 3580 * q^73 - 2588 * q^74 + 3604 * q^75 - 796 * q^76 + 5808 * q^77 - 572 * q^78 + 4944 * q^79 + 2676 * q^80 + 6738 * q^81 - 292 * q^82 + 2336 * q^83 - 5024 * q^84 + 3359 * q^85 - 5108 * q^86 + 9756 * q^87 - 8904 * q^88 - 644 * q^89 - 12448 * q^90 + 2028 * q^91 - 5760 * q^92 - 6644 * q^93 + 2580 * q^94 - 7484 * q^95 + 11036 * q^96 - 5240 * q^97 + 6756 * q^98 - 16916 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(104))\)

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
104.4.a	\(\chi_{104}(1, \cdot)\)	104.4.a.a	1	1
		104.4.a.b	1
		104.4.a.c	2
		104.4.a.d	2
		104.4.a.e	3
104.4.b	\(\chi_{104}(53, \cdot)\)	104.4.b.a	2	1
		104.4.b.b	34
104.4.e	\(\chi_{104}(77, \cdot)\)	104.4.e.a	40	1
104.4.f	\(\chi_{104}(25, \cdot)\)	104.4.f.a	10	1
104.4.i	\(\chi_{104}(9, \cdot)\)	104.4.i.a	2	2
		104.4.i.b	8
		104.4.i.c	12
104.4.k	\(\chi_{104}(31, \cdot)\)	None	0	2
104.4.m	\(\chi_{104}(83, \cdot)\)	104.4.m.a	80	2
104.4.o	\(\chi_{104}(17, \cdot)\)	104.4.o.a	20	2
104.4.r	\(\chi_{104}(29, \cdot)\)	104.4.r.a	80	2
104.4.s	\(\chi_{104}(69, \cdot)\)	104.4.s.a	80	2
104.4.u	\(\chi_{104}(11, \cdot)\)	104.4.u.a	160	4
104.4.w	\(\chi_{104}(7, \cdot)\)	None	0	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(104))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(104)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)