Space of modular forms of level 4, weight 24, and trivial character

• Label: 4.24.a
• Level: $4$
• Weight: $24$
• Character orbit: 4.a
• Rep. character: $\chi_{4}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	4.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(4))\).

	Total	New	Old
Modular forms	13	2	11
Cusp forms	10	2	8
Eisenstein series	3	0	3

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

\(2\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(7\)	\(0\)	\(7\)		\(5\)	\(0\)	\(5\)		\(2\)	\(0\)	\(2\)
\(-\)		\(6\)	\(2\)	\(4\)		\(5\)	\(2\)	\(3\)		\(1\)	\(0\)	\(1\)

Trace form

2 * q + 170520 * q^3 - 92266020 * q^5 + 192083440 * q^7 + 8599879818 * q^9 - 1247174695800 * q^11 - 7460299980980 * q^13 - 106334360092080 * q^15 - 374897347903260 * q^17 - 840360279212552 * q^19 + 400401295079232 * q^21 + 6433357923072720 * q^23 + 33587241295679150 * q^25 + 15773861091124080 * q^27 - 68055499247434452 * q^29 - 145584514546845248 * q^31 - 650343867352613280 * q^33 - 216234488190163680 * q^35 + 1211894143551157660 * q^37 + 3553993994899379088 * q^39 + 5036778367134688692 * q^41 + 935180945919935560 * q^43 - 17187460645010169780 * q^45 - 8431168896277596000 * q^47 - 53910291562566659694 * q^49 - 4938798717170442576 * q^51 + 3763137197370204540 * q^53 + 351301189218989209200 * q^55 - 43703893486254219360 * q^57 + 348561606512901387816 * q^59 - 582966592720711355156 * q^61 + 66309764232647559600 * q^63 - 1918465858864426149720 * q^65 + 211615268845414654360 * q^67 - 1499363181860662472256 * q^69 + 3840047757133544010096 * q^71 - 680666251913594096780 * q^73 + 11948876435052098946600 * q^75 - 1265465342298122095680 * q^77 - 642991395306723640736 * q^79 - 13196380320218478599982 * q^81 - 18799502632508717771400 * q^83 + 2701670550661359899640 * q^85 - 26089604267151850210800 * q^87 + 5001398778883250139732 * q^89 + 8107764572821621082528 * q^91 + 104099589081258166744320 * q^93 + 23677928248035152895120 * q^95 + 122022794260559820614980 * q^97 - 98127319293495379027800 * q^99

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(4))\) 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
4.24.a.a	$4$	$24$	4.a	1.a	$1$	$2$	$2$	$13.408$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	4.24.a.a	$1$	$1$	\(0\)	\(170520\)	\(-92266020\)	\(192083440\)		$-$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(85260-\beta )q^{3}+(-46133010+540\beta )q^{5}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(4)) \simeq \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)