Space of modular forms of level 10 and weight 16

• Label: 10.16
• Level: 10
• Weight: 16
• Dimension: 13
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 96
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	49	13	36
Cusp forms	41	13	28
Eisenstein series	8	0	8

Trace form

13 * q + 128 * q^2 - 9632 * q^3 - 49152 * q^4 + 329525 * q^5 + 374272 * q^6 + 535804 * q^7 + 2097152 * q^8 - 32081191 * q^9 + 14403200 * q^10 + 74291676 * q^11 - 157810688 * q^12 + 744201478 * q^13 - 843293696 * q^14 - 400176200 * q^15 + 3489660928 * q^16 + 890757354 * q^17 + 654709376 * q^18 + 5718256060 * q^19 - 2838937600 * q^20 - 6873116744 * q^21 + 13494391296 * q^22 + 1886355348 * q^23 + 7876902912 * q^24 + 28275723125 * q^25 + 35608306432 * q^26 - 33283167920 * q^27 + 8778612736 * q^28 - 378760754610 * q^29 + 8378457600 * q^30 + 234286501176 * q^31 + 34359738368 * q^32 - 152670425424 * q^33 + 221272455424 * q^34 - 1624581833900 * q^35 + 899500621824 * q^36 + 1660154133694 * q^37 + 376608140800 * q^38 - 5979609034672 * q^39 + 91697971200 * q^40 + 6349243817226 * q^41 + 4441635721216 * q^42 - 2804034484232 * q^43 - 1910039445504 * q^44 - 4111920212175 * q^45 + 7669043950592 * q^46 + 10246116175284 * q^47 - 2585570312192 * q^48 - 22992059603379 * q^49 - 12704292400000 * q^50 + 49649536067936 * q^51 + 12192997015552 * q^52 - 25057737033762 * q^53 - 14762231546880 * q^54 - 33331218511700 * q^55 + 2546093522944 * q^56 + 19903369887200 * q^57 - 10077353329920 * q^58 - 57175150397820 * q^59 - 6735033139200 * q^60 + 85997166482726 * q^61 + 24327579406336 * q^62 + 9069525437468 * q^63 - 13194139533312 * q^64 + 100001032236550 * q^65 - 213315881363456 * q^66 - 98148968872856 * q^67 + 14594168487936 * q^68 + 256643990012968 * q^69 + 16689463987200 * q^70 - 134205399999024 * q^71 + 10726758416384 * q^72 + 66038638669618 * q^73 + 233113673553664 * q^74 + 167659423700000 * q^75 - 118623047843840 * q^76 - 516867155383872 * q^77 + 63914271450112 * q^78 + 1234426966039840 * q^79 + 88456193638400 * q^80 - 1568342837347347 * q^81 - 248954943124224 * q^82 - 169647139364832 * q^83 + 371057201381376 * q^84 + 907859952597850 * q^85 + 9545226445312 * q^86 - 764001995922720 * q^87 + 221092106993664 * q^88 - 560276244969630 * q^89 + 885924008169600 * q^90 - 926840819951464 * q^91 + 30906046021632 * q^92 - 660512111777584 * q^93 - 205082936252416 * q^94 - 1635773250666500 * q^95 + 100467874988032 * q^96 + 1420399684126474 * q^97 - 405707494390656 * q^98 + 3141687217590668 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.16.a	\(\chi_{10}(1, \cdot)\)	10.16.a.a	1	1
		10.16.a.b	1
		10.16.a.c	1
		10.16.a.d	2
10.16.b	\(\chi_{10}(9, \cdot)\)	10.16.b.a	8	1

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)