Space of modular forms of level 2, weight 26, and trivial character

• Label: 2.26.a
• Level: $2$
• Weight: $26$
• Character orbit: 2.a
• Rep. character: $\chi_{2}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $6$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(6\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(2))\).

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

Trace form

3 * q + 4096 * q^2 + 477804 * q^3 + 50331648 * q^4 + 1082958450 * q^5 + 1154629632 * q^6 - 41259174312 * q^7 + 68719476736 * q^8 + 2456838201159 * q^9 + 1642281984000 * q^10 - 6183187766844 * q^11 + 8016220913664 * q^12 - 18623063615286 * q^13 + 165912987336704 * q^14 - 1418778892971000 * q^15 + 844424930131968 * q^16 - 1327546948772682 * q^17 + 16925592224452608 * q^18 - 14476503947047140 * q^19 + 18169027834675200 * q^20 - 98865491287772064 * q^21 + 93508636620275712 * q^22 - 29452245057438456 * q^23 + 19371470736064512 * q^24 + 13625643203968125 * q^25 - 795898030855364608 * q^26 + 2006515475993054520 * q^27 - 692214079414075392 * q^28 + 3804643074807962490 * q^29 - 6084959981978419200 * q^30 - 6024549917048451744 * q^31 + 1152921504606846976 * q^32 - 4777633723177011312 * q^33 + 16315616415746433024 * q^34 + 16630841714950218000 * q^35 + 41218905177895993344 * q^36 - 86287972030065606702 * q^37 + 55387527008863600640 * q^38 - 144889527996244146072 * q^39 + 27552919578476544000 * q^40 + 316574131640178799806 * q^41 - 372146552978360107008 * q^42 + 4406011488742288164 * q^43 - 103736676732899426304 * q^44 + 331401278747581619850 * q^45 - 823942375446566043648 * q^46 + 2149187127091682220048 * q^47 + 134489869772258279424 * q^48 - 524397224512548705429 * q^49 + 1544613042178577920000 * q^50 - 7254340889000213332584 * q^51 - 312443160855394123776 * q^52 - 2817100001721097140606 * q^53 + 9570810422957059768320 * q^54 - 259329155335977018600 * q^55 + 2783558025753147736064 * q^56 + 14809787410741003134960 * q^57 - 1457429644882294087680 * q^58 - 25752580702182118552620 * q^59 - 23803159943615348736000 * q^60 + 58273808422153400946906 * q^61 - 46496213645941973843968 * q^62 - 2378665557655847152776 * q^63 + 14167099448608935641088 * q^64 + 33639177305668163029500 * q^65 - 7928589045076086030336 * q^66 - 91687165138132830937812 * q^67 - 22272541909700220813312 * q^68 + 133545663071151999943968 * q^69 + 182326222209622243737600 * q^70 - 371396990842508553600744 * q^71 + 283964316677561886179328 * q^72 + 353864430262753766920734 * q^73 + 67466215139595328446464 * q^74 - 1162701372097460046907500 * q^75 - 242875433644462429962240 * q^76 + 686668981303319284175136 * q^77 - 663958403786416396468224 * q^78 + 123276068749625658422640 * q^79 + 304825704492358120243200 * q^80 + 2602795698165838861769643 * q^81 - 616634298074201546907648 * q^82 - 443559281547277297098276 * q^83 - 1658687702281070076493824 * q^84 + 1934938263012912585418500 * q^85 + 346821450457913407619072 * q^86 - 6460593803049848600508120 * q^87 + 1568814594443875599777792 * q^88 + 1209100457235696633777870 * q^89 + 3697528938303212522496000 * q^90 - 1001998704753591930702384 * q^91 - 494126677013577383018496 * q^92 - 1627354974425964978364032 * q^93 + 6510732644424363948048384 * q^94 - 10222902461728178016279000 * q^95 + 324999348776633307758592 * q^96 + 4984992770493732599418918 * q^97 - 4853924091950689643163648 * q^98 + 23986549987983068504983668 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(2))\) 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
2.26.a.a	$2$	$26$	2.a	1.a	$1$	$1$	$1$	$7.920$	\(\Q\)	None	✓	✓	✓	✓	2.26.a.a	$1$	$1$	\(-4096\)	\(97956\)	\(341005350\)	\(-40882637368\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{12}q^{2}+97956q^{3}+2^{24}q^{4}+341005350q^{5}+\cdots\)
2.26.a.b	$2$	$26$	2.a	1.a	$1$	$2$	$2$	$7.920$	\(\Q(\sqrt{106705}) \)	None	✓	✓	✓	✓	2.26.a.b	$1$	$0$	\(8192\)	\(379848\)	\(741953100\)	\(-376536944\)		$-$	$-$	$2^{7}\cdot 3\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+2^{12}q^{2}+(189924-\beta )q^{3}+2^{24}q^{4}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(2)) \simeq \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)