Space of modular forms of level 2, weight 18, and trivial character

• Label: 2.18.a
• Level: $2$
• Weight: $18$
• Character orbit: 2.a
• Rep. character: $\chi_{2}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(2))\).

	Total	New	Old
Modular forms	5	1	4
Cusp forms	3	1	2
Eisenstein series	2	0	2

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
\(+\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)

Trace form

q + 256 * q^2 + 6084 * q^3 + 65536 * q^4 + 1255110 * q^5 + 1557504 * q^6 - 22465912 * q^7 + 16777216 * q^8 - 92125107 * q^9 + 321308160 * q^10 + 172399692 * q^11 + 398721024 * q^12 - 2180149426 * q^13 - 5751273472 * q^14 + 7636089240 * q^15 + 4294967296 * q^16 + 30163933458 * q^17 - 23584027392 * q^18 - 76275766060 * q^19 + 82254888960 * q^20 - 136682608608 * q^21 + 44134321152 * q^22 + 130466597784 * q^23 + 102072582144 * q^24 + 812361658975 * q^25 - 558118253056 * q^26 - 1346177902680 * q^27 - 1472326008832 * q^28 + 803134463070 * q^29 + 1954838845440 * q^30 + 2045336056352 * q^31 + 1099511627776 * q^32 + 1048879726128 * q^33 + 7721966965248 * q^34 - 28197190810320 * q^35 - 6037511012352 * q^36 + 33855367078118 * q^37 - 19526596111360 * q^38 - 13264029107784 * q^39 + 21057251573760 * q^40 + 53206442755242 * q^41 - 34990747803648 * q^42 + 26590357792364 * q^43 + 11298386214912 * q^44 - 115627143046770 * q^45 + 33399449032704 * q^46 - 232565394320592 * q^47 + 26130581028864 * q^48 + 272086688004537 * q^49 + 207964584697600 * q^50 + 183517371158472 * q^51 - 142878272782336 * q^52 - 163277861935626 * q^53 - 344621543086080 * q^54 + 216380577426120 * q^55 - 376915458260992 * q^56 - 464061760709040 * q^57 + 205602422545920 * q^58 + 697820734313340 * q^59 + 500438744432640 * q^60 - 898968337037698 * q^61 + 523606030426112 * q^62 + 2069674546852584 * q^63 + 281474976710656 * q^64 - 2736327346066860 * q^65 + 268513209888768 * q^66 - 2667002109080572 * q^67 + 1976823543103488 * q^68 + 793758780917856 * q^69 - 7218480847441920 * q^70 + 3910637666678472 * q^71 - 1545602819162112 * q^72 + 5855931724867274 * q^73 + 8666973971998208 * q^74 + 4942408333203900 * q^75 - 4998808604508160 * q^76 - 3873116309299104 * q^77 - 3395591451592704 * q^78 - 23821740190145200 * q^79 + 5390656402882560 * q^80 + 3706904974467321 * q^81 + 13620849345341952 * q^82 - 13915745478008556 * q^83 - 8957631437733888 * q^84 + 37859054522470380 * q^85 + 6807131594845184 * q^86 + 4886270073317880 * q^87 + 2892386871017472 * q^88 - 30722744829110310 * q^89 - 29600548619973120 * q^90 + 48979045151366512 * q^91 + 8550258952372224 * q^92 + 12443824566845568 * q^93 - 59536740946071552 * q^94 - 95734476739566600 * q^95 + 6689428743389184 * q^96 + 57649100896826978 * q^97 + 69654192129161472 * q^98 - 15882340072267044 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(2))\) 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
2.18.a.a	$2$	$18$	2.a	1.a	$1$	$1$	$1$	$3.664$	\(\Q\)	None	✓	✓	✓	✓	2.18.a.a	$1$	$0$	\(256\)	\(6084\)	\(1255110\)	\(-22465912\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{8}q^{2}+78^{2}q^{3}+2^{16}q^{4}+1255110q^{5}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

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