Space of modular forms of level 18, weight 14, and trivial character

• Label: 18.14.a
• Level: $18$
• Weight: $14$
• Character orbit: 18.a
• Rep. character: $\chi_{18}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $5$
• Sturm bound: $42$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	18.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(42\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(18))\).

	Total	New	Old
Modular forms	43	5	38
Cusp forms	35	5	30
Eisenstein series	8	0	8

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

\(2\)	\(3\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(10\)	\(1\)	\(9\)		\(8\)	\(1\)	\(7\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(11\)	\(2\)	\(9\)		\(9\)	\(2\)	\(7\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(11\)	\(1\)	\(10\)		\(9\)	\(1\)	\(8\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(11\)	\(1\)	\(10\)		\(9\)	\(1\)	\(8\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(21\)	\(2\)	\(19\)		\(17\)	\(2\)	\(15\)		\(4\)	\(0\)	\(4\)
Minus space		\(-\)		\(22\)	\(3\)	\(19\)		\(18\)	\(3\)	\(15\)		\(4\)	\(0\)	\(4\)

Trace form

5 * q - 64 * q^2 + 20480 * q^4 - 1194 * q^5 + 3640 * q^7 - 262144 * q^8 + 1605504 * q^10 - 10696764 * q^11 + 17757934 * q^13 - 43136000 * q^14 + 83886080 * q^16 + 22983354 * q^17 - 65305772 * q^19 - 4890624 * q^20 + 268562688 * q^22 + 2145617400 * q^23 + 707878883 * q^25 + 327535744 * q^26 + 14909440 * q^28 - 1563969954 * q^29 + 9858963184 * q^31 - 1073741824 * q^32 + 6512257152 * q^34 - 4217945664 * q^35 - 14479577522 * q^37 - 36448235264 * q^38 + 6576144384 * q^40 + 92053598322 * q^41 - 93159221108 * q^43 - 43813945344 * q^44 + 77158000128 * q^46 + 129804728640 * q^47 - 242054707683 * q^49 - 323260095424 * q^50 + 72736497664 * q^52 + 120318145686 * q^53 + 174302282952 * q^55 - 176685056000 * q^56 + 144695845248 * q^58 - 41683896060 * q^59 + 175311584518 * q^61 - 587745715712 * q^62 + 343597383680 * q^64 + 1818167249652 * q^65 - 563821954652 * q^67 + 94139817984 * q^68 + 691726129152 * q^70 + 1129713436296 * q^71 - 1107232658198 * q^73 - 220869064064 * q^74 - 267492442112 * q^76 - 622251064320 * q^77 + 5731459525120 * q^79 - 20031995904 * q^80 - 2303842591104 * q^82 - 9508876592772 * q^83 - 8378520431148 * q^85 + 5663394995968 * q^86 + 1100032770048 * q^88 - 8719146589518 * q^89 + 5379105430640 * q^91 + 8788448870400 * q^92 - 20387639691264 * q^94 - 1583506373304 * q^95 + 24942206614306 * q^97 + 15970059155904 * q^98

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(18))\) 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	3
18.14.a.a	$18$	$14$	18.a	1.a	$1$	$1$	$1$	$19.302$	\(\Q\)	None	✓				6.14.a.a	$1$	$0$	\(-64\)	\(0\)	\(-54654\)	\(176336\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{6}q^{2}+2^{12}q^{4}-54654q^{5}+176336q^{7}+\cdots\)
18.14.a.b	$18$	$14$	18.a	1.a	$1$	$1$	$1$	$19.302$	\(\Q\)	None	✓	✓	✓	✓	18.14.a.b	$1$	$1$	\(-64\)	\(0\)	\(-15936\)	\(98252\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{6}q^{2}+2^{12}q^{4}-15936q^{5}+98252q^{7}+\cdots\)
18.14.a.c	$18$	$14$	18.a	1.a	$1$	$1$	$1$	$19.302$	\(\Q\)	None	✓				2.14.a.b	$1$	$0$	\(-64\)	\(0\)	\(57450\)	\(64232\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{6}q^{2}+2^{12}q^{4}+57450q^{5}+64232q^{7}+\cdots\)
18.14.a.d	$18$	$14$	18.a	1.a	$1$	$1$	$1$	$19.302$	\(\Q\)	None	✓		✓	✓	2.14.a.a	$1$	$1$	\(64\)	\(0\)	\(-3990\)	\(-433432\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{6}q^{2}+2^{12}q^{4}-3990q^{5}-433432q^{7}+\cdots\)
18.14.a.e	$18$	$14$	18.a	1.a	$1$	$1$	$1$	$19.302$	\(\Q\)	None	✓	✓	✓	✓	18.14.a.b	$1$	$0$	\(64\)	\(0\)	\(15936\)	\(98252\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{6}q^{2}+2^{12}q^{4}+15936q^{5}+98252q^{7}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(18)) \simeq \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)