Space of modular forms of level 4, weight 18, and trivial character

• Label: 4.18.a
• Level: $4$
• Weight: $18$
• Character orbit: 4.a
• Rep. character: $\chi_{4}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	4.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(4))\).

	Total	New	Old
Modular forms	10	2	8
Cusp forms	7	2	5
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
\(+\)		\(5\)	\(0\)	\(5\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)
\(-\)		\(5\)	\(2\)	\(3\)		\(4\)	\(2\)	\(2\)		\(1\)	\(0\)	\(1\)

Trace form

2 * q - 5880 * q^3 + 604044 * q^5 + 25350160 * q^7 + 449174682 * q^9 + 1259648280 * q^11 - 1320052580 * q^13 - 26621930448 * q^15 - 27498226140 * q^17 + 101133633832 * q^19 + 335430207552 * q^21 + 134767491120 * q^23 - 448986850114 * q^25 - 4619416117680 * q^27 + 2337155582652 * q^29 + 278836113472 * q^31 + 22602380058720 * q^33 - 7102242382752 * q^35 + 20929802888140 * q^37 - 108447997173648 * q^39 + 4166592315732 * q^41 - 111143148534440 * q^43 + 281755357404444 * q^45 + 196772651157600 * q^47 + 99570326741874 * q^49 - 39956666918256 * q^51 - 487965122736660 * q^53 - 566565363246960 * q^55 - 2272313631999840 * q^57 + 2835904197813624 * q^59 - 67544034994436 * q^61 + 3282762121966800 * q^63 + 3645157343001768 * q^65 - 995171321546360 * q^67 - 10188302100105024 * q^69 + 3882245493215376 * q^71 - 12746425881769580 * q^73 - 13688080703624712 * q^75 + 31591755846002880 * q^77 - 14984271534065504 * q^79 + 33380230287529458 * q^81 + 43899417809893800 * q^83 - 3956216991540264 * q^85 - 100892756486768400 * q^87 + 51909007958846388 * q^89 - 83455169400462112 * q^91 - 89807116632334080 * q^93 + 101643889304423664 * q^95 - 49281007789848380 * q^97 + 128223271309133880 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(4))\) 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
4.18.a.a	$4$	$18$	4.a	1.a	$1$	$2$	$2$	$7.329$	\(\Q(\sqrt{9361}) \)	None	✓	✓	✓	✓	4.18.a.a	$1$	$0$	\(0\)	\(-5880\)	\(604044\)	\(25350160\)		$-$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-2940-\beta )q^{3}+(302022+6^{2}\beta )q^{5}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(4)) \simeq \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)