Space of modular forms of level 10, weight 24, and trivial character

• Label: 10.24.a
• Level: $10$
• Weight: $24$
• Character orbit: 10.a
• Rep. character: $\chi_{10}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $4$
• Sturm bound: $36$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(36\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(10))\).

	Total	New	Old
Modular forms	37	9	28
Cusp forms	33	9	24
Eisenstein series	4	0	4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(5\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(-\)	\(-\)	\(2\)
\(-\)	\(+\)	\(-\)	\(2\)
\(-\)	\(-\)	\(+\)	\(3\)
Plus space		\(+\)	\(5\)
Minus space		\(-\)	\(4\)

Trace form

9 * q + 2048 * q^2 + 346108 * q^3 + 37748736 * q^4 + 48828125 * q^5 - 2027167744 * q^6 - 8876639496 * q^7 + 8589934592 * q^8 + 273896693533 * q^9 + 100000000000 * q^10 - 42346698492 * q^11 + 1451682168832 * q^12 + 9813380914758 * q^13 + 14364714876928 * q^14 - 41166601562500 * q^15 + 158329674399744 * q^16 + 72601975229634 * q^17 + 172043830962176 * q^18 - 677858882796900 * q^19 + 204800000000000 * q^20 - 1030253335521712 * q^21 - 4721655230029824 * q^22 + 16657686570156168 * q^23 - 8502557777330176 * q^24 + 21457672119140625 * q^25 - 31286636523474944 * q^26 + 40764097342433080 * q^27 - 37231324544630784 * q^28 + 86482023852036390 * q^29 + 56690800000000000 * q^30 - 134645415979796832 * q^31 + 36028797018963968 * q^32 - 94263270072397104 * q^33 - 384033444848627712 * q^34 - 298318705859375000 * q^35 + 1148805997272236032 * q^36 + 642486984951409134 * q^37 - 328721663926476800 * q^38 + 4395795394947629576 * q^39 + 419430400000000000 * q^40 + 8428662504456387258 * q^41 + 10106612710568820736 * q^42 - 5404897877223011532 * q^43 - 177614926871789568 * q^44 - 1943976970849609375 * q^45 + 2956922280193867776 * q^46 - 46261143731970128496 * q^47 + 6088796327460732928 * q^48 + 35274325969329515457 * q^49 + 4882812500000000000 * q^50 + 42098910347460957048 * q^51 + 41160302824293138432 * q^52 + 17569459772978062878 * q^53 - 232823977912675287040 * q^54 - 25921977274804687500 * q^55 + 60249981067158618112 * q^56 + 385332070284848085200 * q^57 - 179583090098983096320 * q^58 - 138143426689104647820 * q^59 - 172665241600000000000 * q^60 + 720429521517235121718 * q^61 + 190054974949529092096 * q^62 - 4168870810602313550152 * q^63 + 664082786653543858176 * q^64 - 326826526837988281250 * q^65 + 2191081594490397622272 * q^66 + 1636606502936345345724 * q^67 + 304514755113554804736 * q^68 - 1748264848232192569104 * q^69 - 433728709600000000000 * q^70 + 464954138759430178488 * q^71 + 721604128379978645504 * q^72 - 3451992448263413827062 * q^73 - 1092732528041154547712 * q^74 + 825185775756835937500 * q^75 - 2843146223550568857600 * q^76 + 24137009187432595030848 * q^77 - 6521850729612988694528 * q^78 - 19117353847012063634640 * q^79 + 858993459200000000000 * q^80 + 17780761156422767784769 * q^81 + 31328326113498215141376 * q^82 - 40379114385537009437172 * q^83 - 4321195686192058728448 * q^84 + 12798831015099316406250 * q^85 + 20315042123786905624576 * q^86 + 96611009127715382594280 * q^87 - 19804057417935010922496 * q^88 - 115629362568723625840710 * q^89 + 44634134163700000000000 * q^90 - 75999124804313689800912 * q^91 + 69867401411952296067072 * q^92 - 22644525669600692370784 * q^93 - 104738781963437193756672 * q^94 + 86760091183237304687500 * q^95 - 35662312095687066517504 * q^96 + 252902466646785784930194 * q^97 - 24904249932481475229696 * q^98 - 588914835717122042186604 * q^99

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(10))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5
10.24.a.a	$10$	$24$	10.a	1.a	$1$	$2$	$2$	$33.520$	\(\Q(\sqrt{219241}) \)	None	✓	✓	✓	✓	10.24.a.a	$1$	$1$	\(-4096\)	\(-18516\)	\(97656250\)	\(-4415735108\)		$+$	$-$	$-$	$2^{2}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q-2^{11}q^{2}+(-9258-17\beta )q^{3}+2^{22}q^{4}+\cdots\)
10.24.a.b	$10$	$24$	10.a	1.a	$1$	$2$	$2$	$33.520$	\(\Q(\sqrt{117349}) \)	None	✓	✓	✓	✓	10.24.a.b	$1$	$0$	\(-4096\)	\(686484\)	\(-97656250\)	\(-3529595108\)		$+$	$+$	$+$	$2^{5}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q-2^{11}q^{2}+(343242-3\beta )q^{3}+2^{22}q^{4}+\cdots\)
10.24.a.c	$10$	$24$	10.a	1.a	$1$	$2$	$2$	$33.520$	\(\Q(\sqrt{1492261}) \)	None	✓	✓	✓	✓	10.24.a.c	$1$	$1$	\(4096\)	\(-91884\)	\(-97656250\)	\(2146058908\)		$-$	$+$	$-$	$2^{5}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{11}q^{2}+(-45942-\beta )q^{3}+2^{22}q^{4}+\cdots\)
10.24.a.d	$10$	$24$	10.a	1.a	$1$	$3$	$3$	$33.520$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	10.24.a.d	$1$	$0$	\(6144\)	\(-229976\)	\(146484375\)	\(-3077368188\)		$-$	$-$	$+$	$2^{9}\cdot 3\cdot 5^{3}$	$\mathrm{SU}(2)$	\(q+2^{11}q^{2}+(-76659-\beta _{1})q^{3}+2^{22}q^{4}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(10))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(10)) \simeq \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)