Space of modular forms of level 169 and weight 10

• Label: 169.10
• Level: 169
• Weight: 10
• Dimension: 10419
• Nonzero newspaces: 8
• Sturm bound: 23660
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 169 = 13^{2} \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(23660\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(169))\).

	Total	New	Old
Modular forms	10761	10624	137
Cusp forms	10533	10419	114
Eisenstein series	228	205	23

Trace form

10419 * q - 66 * q^2 - 66 * q^3 - 66 * q^4 - 66 * q^5 - 66 * q^6 + 4038 * q^7 + 73662 * q^8 - 66 * q^9 - 306786 * q^10 + 36774 * q^11 + 829386 * q^12 + 108360 * q^13 - 727806 * q^14 - 1193682 * q^15 - 66 * q^16 + 2815332 * q^17 - 1992198 * q^18 + 1891830 * q^19 - 95058 * q^20 - 2184066 * q^21 - 14502606 * q^22 - 2158314 * q^23 + 19398942 * q^24 + 11718696 * q^25 + 8735178 * q^26 - 6678774 * q^27 - 28478646 * q^28 - 48742500 * q^29 - 11197218 * q^30 + 43257486 * q^31 + 104870010 * q^32 + 34107534 * q^33 - 76366962 * q^34 - 125492706 * q^35 - 69537066 * q^36 + 107018004 * q^37 + 150129738 * q^38 + 80178864 * q^39 - 213193422 * q^40 - 113494152 * q^41 + 29052762 * q^42 + 160350054 * q^43 - 113669622 * q^44 - 146879016 * q^45 - 340457754 * q^46 + 12327606 * q^47 + 113874462 * q^48 + 69698166 * q^49 + 257217330 * q^50 + 143171274 * q^51 + 288763590 * q^52 + 228379434 * q^53 + 492983490 * q^54 - 327790074 * q^55 - 822907062 * q^56 - 1131415242 * q^57 - 1075604034 * q^58 - 308757690 * q^59 + 121664658 * q^60 + 1564547880 * q^61 + 2017677342 * q^62 - 201404202 * q^63 - 1101924774 * q^64 - 106769511 * q^65 + 2710233306 * q^66 + 2485367838 * q^67 + 672525450 * q^68 - 2199370122 * q^69 - 4608699990 * q^70 - 3093851250 * q^71 - 5102810694 * q^72 - 259608162 * q^73 + 1009589814 * q^74 + 2605971210 * q^75 + 4482522966 * q^76 + 4653806154 * q^77 + 3971344830 * q^78 + 1667535810 * q^79 - 6110622 * q^80 - 1428453054 * q^81 - 5229320154 * q^82 - 7686015858 * q^83 - 13626100902 * q^84 - 2534884032 * q^85 - 5986033374 * q^86 - 5033253642 * q^87 + 10703372970 * q^88 + 10695147534 * q^89 + 32397195858 * q^90 + 6798799020 * q^91 + 5434586946 * q^92 - 4784070234 * q^93 - 17332218762 * q^94 - 15243614778 * q^95 - 20018064966 * q^96 - 9419334330 * q^97 - 17393800026 * q^98 - 14821060410 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(169))\)

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
169.10.a	\(\chi_{169}(1, \cdot)\)	169.10.a.a	4	1
		169.10.a.b	5
		169.10.a.c	9
		169.10.a.d	9
		169.10.a.e	10
		169.10.a.f	20
		169.10.a.g	27
		169.10.a.h	27
169.10.b	\(\chi_{169}(168, \cdot)\)	n/a	110	1
169.10.c	\(\chi_{169}(22, \cdot)\)	n/a	222	2
169.10.e	\(\chi_{169}(23, \cdot)\)	n/a	220	2
169.10.g	\(\chi_{169}(14, \cdot)\)	n/a	1620	12
169.10.h	\(\chi_{169}(12, \cdot)\)	n/a	1632	12
169.10.i	\(\chi_{169}(3, \cdot)\)	n/a	3240	24
169.10.k	\(\chi_{169}(4, \cdot)\)	n/a	3264	24

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(169))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(169)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)