Space of modular forms of level 104 and weight 10

• Label: 104.10
• Level: 104
• Weight: 10
• Dimension: 1657
• Nonzero newspaces: 10
• Sturm bound: 6720
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 10 \)
Sturm bound:			\(6720\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(104))\).

	Total	New	Old
Modular forms	3096	1701	1395
Cusp forms	2952	1657	1295
Eisenstein series	144	44	100

Trace form

1657 * q + 24 * q^2 - 28 * q^3 + 844 * q^4 + 1128 * q^5 - 9380 * q^6 - 21420 * q^7 + 6756 * q^8 + 140996 * q^9 - 52796 * q^10 - 195132 * q^11 - 109532 * q^12 + 188836 * q^13 + 144648 * q^14 - 127980 * q^15 - 371244 * q^16 - 285891 * q^17 + 47216 * q^18 - 1732040 * q^19 - 2490540 * q^20 + 1214952 * q^21 + 4746236 * q^22 - 539544 * q^23 + 7922900 * q^24 - 6363283 * q^25 - 4551252 * q^26 + 3772292 * q^27 - 15019852 * q^28 + 8662185 * q^29 + 30568724 * q^30 + 3244616 * q^31 + 28226484 * q^32 - 21004336 * q^33 - 55514500 * q^34 - 17475384 * q^35 - 114216192 * q^36 - 7812747 * q^37 + 127322268 * q^38 + 86391888 * q^39 - 62234280 * q^40 + 25988241 * q^41 - 2539604 * q^42 + 101660276 * q^43 - 152313552 * q^44 - 127227059 * q^45 - 295478404 * q^46 - 19449384 * q^47 + 235781652 * q^48 - 115882016 * q^49 + 80442492 * q^50 + 428564392 * q^51 + 422868256 * q^52 + 13594668 * q^53 + 467233928 * q^54 - 167770212 * q^55 - 406612224 * q^56 - 521070252 * q^57 - 1243773628 * q^58 - 236841240 * q^59 + 422354124 * q^60 + 835711949 * q^61 + 1654639176 * q^62 + 1544369068 * q^63 - 672306500 * q^64 - 219952659 * q^65 - 1421757048 * q^66 + 113710552 * q^67 - 159750108 * q^68 + 347896988 * q^69 + 135841584 * q^70 - 497865564 * q^71 - 224546044 * q^72 + 1803583216 * q^73 + 131547204 * q^74 - 727367156 * q^75 + 175065508 * q^76 - 954029232 * q^77 - 318117980 * q^78 + 69871952 * q^79 - 1780882572 * q^80 - 196815612 * q^81 + 2103962332 * q^82 + 3576766344 * q^83 + 2066974240 * q^84 + 1957726657 * q^85 + 505917420 * q^86 - 9848066004 * q^87 - 300925576 * q^88 - 3303741312 * q^89 - 5824838368 * q^90 + 9085328796 * q^91 + 1474056576 * q^92 + 4176722596 * q^93 - 3089617260 * q^94 - 7309825356 * q^95 + 10840200092 * q^96 - 3525846908 * q^97 + 12967203684 * q^98 - 1540380092 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(104))\)

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
104.10.a	\(\chi_{104}(1, \cdot)\)	104.10.a.a	6	1
		104.10.a.b	6
		104.10.a.c	7
		104.10.a.d	8
104.10.b	\(\chi_{104}(53, \cdot)\)	n/a	108	1
104.10.e	\(\chi_{104}(77, \cdot)\)	n/a	124	1
104.10.f	\(\chi_{104}(25, \cdot)\)	104.10.f.a	32	1
104.10.i	\(\chi_{104}(9, \cdot)\)	104.10.i.a	30	2
		104.10.i.b	32
104.10.k	\(\chi_{104}(31, \cdot)\)	None	0	2
104.10.m	\(\chi_{104}(83, \cdot)\)	n/a	248	2
104.10.o	\(\chi_{104}(17, \cdot)\)	104.10.o.a	64	2
104.10.r	\(\chi_{104}(29, \cdot)\)	n/a	248	2
104.10.s	\(\chi_{104}(69, \cdot)\)	n/a	248	2
104.10.u	\(\chi_{104}(11, \cdot)\)	n/a	496	4
104.10.w	\(\chi_{104}(7, \cdot)\)	None	0	4

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(104))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(104)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)