Space of modular forms of level 10 and weight 24

• Label: 10.24
• Level: 10
• Weight: 24
• Dimension: 21
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 144
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 24 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	73	21	52
Cusp forms	65	21	44
Eisenstein series	8	0	8

Trace form

21 * q + 2048 * q^2 + 346108 * q^3 - 12582912 * q^4 - 104637535 * q^5 - 530948096 * q^6 - 8876639496 * q^7 + 8589934592 * q^8 - 123508182991 * q^9 + 615607920640 * q^10 + 1576361769972 * q^11 + 1451682168832 * q^12 + 9813380914758 * q^13 - 4247764484096 * q^14 + 15194258294860 * q^15 + 369435906932736 * q^16 + 72601975229634 * q^17 + 172043830962176 * q^18 - 1778121289351380 * q^19 + 848481631600640 * q^20 + 1424441653683712 * q^21 - 4721655230029824 * q^22 + 16657686570156168 * q^23 - 14778157831815168 * q^24 + 39805718715259725 * q^25 + 16125498490630144 * q^26 + 40764097342433080 * q^27 - 37231324544630784 * q^28 - 104850094542814290 * q^29 + 125753066581647360 * q^30 + 179886204782396832 * q^31 + 36028797018963968 * q^32 - 94263270072397104 * q^33 - 411235864196837376 * q^34 - 431292273365424680 * q^35 + 2815642860496355328 * q^36 + 642486984951409134 * q^37 - 328721663926476800 * q^38 + 21197039311855286888 * q^39 - 1743185963972034560 * q^40 + 8093925990635214162 * q^41 + 10106612710568820736 * q^42 - 5404897877223011532 * q^43 - 6966970330984218624 * q^44 + 42627532206788264445 * q^45 + 40001719905871478784 * q^46 - 46261143731970128496 * q^47 + 6088796327460732928 * q^48 - 26078708780322755739 * q^49 - 6605853940926822400 * q^50 + 63893328704733896312 * q^51 + 41160302824293138432 * q^52 + 17569459772978062878 * q^53 - 297307221394282659840 * q^54 + 7686640642786294980 * q^55 + 138316377701019025408 * q^56 + 385332070284848085200 * q^57 - 179583090098983096320 * q^58 - 930634508938186386780 * q^59 - 409059821543164477440 * q^60 + 1117303311048918638622 * q^61 + 190054974949529092096 * q^62 - 4168870810602313550152 * q^63 - 221360928884514619392 * q^64 - 1430291433259505873090 * q^65 + 271779070976175996928 * q^66 + 1636606502936345345724 * q^67 + 304514755113554804736 * q^68 - 6752353014532105730912 * q^69 + 1115699048540305080320 * q^70 + 11681001066382859396952 * q^71 + 721604128379978645504 * q^72 - 3451992448263413827062 * q^73 - 8791581304027817086976 * q^74 + 3523243603152336179900 * q^75 + 1771688789310512824320 * q^76 + 24137009187432595030848 * q^77 - 6521850729612988694528 * q^78 - 32425737356536544010000 * q^79 - 1840802982949090754560 * q^80 + 97811900445140946594621 * q^81 + 31328326113498215141376 * q^82 - 40379114385537009437172 * q^83 - 14616932698196325433344 * q^84 - 41132487193591640254230 * q^85 + 91149962525615333515264 * q^86 + 96611009127715382594280 * q^87 - 19804057417935010922496 * q^88 - 89080032839877345274830 * q^89 - 105201022090550257121280 * q^90 + 137312888888806730263632 * q^91 + 69867401411952296067072 * q^92 - 22644525669600692370784 * q^93 - 215425929513019170717696 * q^94 - 247222889847063227596100 * q^95 - 9340537684760446631936 * q^96 + 252902466646785784930194 * q^97 - 24904249932481475229696 * q^98 - 1086556818723090218656732 * q^99

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.24.a	\(\chi_{10}(1, \cdot)\)	10.24.a.a	2	1
		10.24.a.b	2
		10.24.a.c	2
		10.24.a.d	3
10.24.b	\(\chi_{10}(9, \cdot)\)	10.24.b.a	12	1

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)