Space of modular forms of level 3, weight 44, and trivial character

• Label: 3.44.a
• Level: $3$
• Weight: $44$
• Character orbit: 3.a
• Rep. character: $\chi_{3}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $2$
• Sturm bound: $14$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(14\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{44}(\Gamma_0(3))\).

	Total	New	Old
Modular forms	15	7	8
Cusp forms	13	7	6
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.

\(3\)	Dim
\(+\)	\(4\)
\(-\)	\(3\)

Trace form

7 * q + 6517038 * q^2 - 10460353203 * q^3 + 27552692534980 * q^4 + 1142897486431650 * q^5 + 33441853793523030 * q^6 - 1518687877922879560 * q^7 + 89162849355444024504 * q^8 + 765932923920586514463 * q^9 + 3072194289085163902740 * q^10 - 19035765706499831738724 * q^11 - 325471887738193227553548 * q^12 - 2617160217501477947686246 * q^13 - 22940835489552033441320736 * q^14 - 22577669540410756207434570 * q^15 + 288968962871170267541644816 * q^16 + 132894232119725057809930494 * q^17 + 713087710091653042434702942 * q^18 - 5821548062418507223994361052 * q^19 - 11361818898070054340117998440 * q^20 - 18281043905959596222646348248 * q^21 - 98391603692820471055636363992 * q^22 - 50939297339004823737048394440 * q^23 - 698441214009721194959001259176 * q^24 + 3988249344494775779307363017425 * q^25 + 7876043696489369220439735673364 * q^26 - 1144561273430837494885949696427 * q^27 - 50172114989349391656965649419200 * q^28 + 21862341772501438182015618112506 * q^29 - 79978769266496152864435752377340 * q^30 + 96284802644006465760845197742288 * q^31 + 1085000407788608986452656443411680 * q^32 - 381448984862347506928657111335948 * q^33 - 1717914447357080006255834378640420 * q^34 - 2846930853668343686195953055547120 * q^35 + 3014787765028878333055422557630820 * q^36 + 11827942294905789469146681908011250 * q^37 + 18949776129019716968988077720644248 * q^38 + 6564786091327381994846895875601438 * q^39 + 120952775831830557694116594743526480 * q^40 - 159660757593698934702193525404638922 * q^41 + 41782017368824130786695041362790240 * q^42 - 445385053821651313603552457774294788 * q^43 + 514771999191844202349244122049730352 * q^44 + 125054687646297505376512358426564850 * q^45 + 1919913529753176286697775003240723888 * q^46 + 1007386372706766980950842143847661776 * q^47 - 2528200230117957060664761051515338032 * q^48 - 3134434768153824860259922682917637217 * q^49 - 215835506759972611665719817470649150 * q^50 - 4748262629032092633291700441781677974 * q^51 + 5928474039780845142980093577783102104 * q^52 - 37123865678022673989384726402380809230 * q^53 + 3659173836771121779525330038974083270 * q^54 + 25137017157329762212611755271169823880 * q^55 - 52731379615541759245045493678855898240 * q^56 - 6618467412659334504124654801940360628 * q^57 + 331896989149921437949417385049369480036 * q^58 - 209295975577175279210608813015855660308 * q^59 - 297902712533327459906118070732244448840 * q^60 - 370211751147778043692096224549283789078 * q^61 + 762371962973790329183593532367846459120 * q^62 - 166173292408603127151712517494363868040 * q^63 + 2808223714597123329186355443560276247616 * q^64 + 625625274103466076579712839407412892140 * q^65 - 2578994607297142277040339530297057413368 * q^66 + 2322037304336064260539793412484562855924 * q^67 - 8446047834679208486952132913331032294776 * q^68 + 2934127570990444387065783796502603683944 * q^69 - 12130582077585371798236302781268995312320 * q^70 + 15241554579473183067868746037765841779944 * q^71 + 9756108844558003479850015126262646057336 * q^72 + 36750445086504587297962708685796828639350 * q^73 - 26735922391585513239864278098991204112156 * q^74 - 3529415151601739577719021862742682341125 * q^75 - 130858737506455417609661427645819982824112 * q^76 - 54723580632550426020219452913802424424480 * q^77 - 45251165210554144177882275276918866663676 * q^78 - 62285506214556153263852659257744365976640 * q^79 + 473370600052077409250985876263720552715360 * q^80 + 83807606277934138520219180187019329739767 * q^81 - 60325172294638954945820531986037624103540 * q^82 + 297775298846470618033245296257764909541476 * q^83 + 347336094199013425123163701821074057852736 * q^84 - 388659198907389679147824610988098149552540 * q^85 - 593945295228698781571501136249070550466904 * q^86 - 819521803998802443677617111025903237246466 * q^87 + 651649734797744001253688844880958828678304 * q^88 - 376887070672087582858715444216705586586362 * q^89 + 336156393527303888043111593029783219332660 * q^90 + 1120334119952645800083619159231904049934288 * q^91 + 3252061132085359551594317108350167852059040 * q^92 - 2198554284804227085242625094453339705081680 * q^93 - 4869124258648927645343432668946339360463552 * q^94 + 8450283823986855920702119042300320211171320 * q^95 - 17424290501374393618143926382189653236318368 * q^96 + 1062362705477408245549478273344689659661614 * q^97 + 4229065919565839963906007000405390204075486 * q^98 - 2082874240949520774932861767757129723309316 * q^99

Decomposition of \(S_{44}^{\mathrm{new}}(\Gamma_0(3))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3
3.44.a.a	$3$	$44$	3.a	1.a	$1$	$3$	$3$	$35.133$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	3.44.a.a	$1$	$1$	\(4857024\)	\(31381059609\)	\(-50\!\cdots\!70\)	\(-16\!\cdots\!88\)		$-$	$-$	$2^{13}\cdot 3^{5}\cdot 5\cdot 11$	$\mathrm{SU}(2)$	\(q+(1619008-\beta _{1})q^{2}+3^{21}q^{3}+(-593686009856+\cdots)q^{4}+\cdots\)
3.44.a.b	$3$	$44$	3.a	1.a	$1$	$4$	$4$	$35.133$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓	✓	3.44.a.b	$1$	$0$	\(1660014\)	\(-41841412812\)	\(16\!\cdots\!20\)	\(11\!\cdots\!28\)		$+$	$+$	$2^{14}\cdot 3^{10}\cdot 5^{2}\cdot 7\cdot 11$	$\mathrm{SU}(2)$	\(q+(415003+\beta _{1})q^{2}-3^{21}q^{3}+(7333437011374+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{44}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces

\( S_{44}^{\mathrm{old}}(\Gamma_0(3)) \simeq \) \(S_{44}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)