Space of modular forms of level 3, weight 67, and Character 3.b

• Label: 3.67.b
• Level: $3$
• Weight: $67$
• Character orbit: 3.b
• Rep. character: $\chi_{3}(2,\cdot)$
• Character field: $\Q$
• Dimension: $21$
• Newform subspaces: $2$
• Sturm bound: $22$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 67 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(22\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{67}(3, [\chi])\).

	Total	New	Old
Modular forms	23	23	0
Cusp forms	21	21	0
Eisenstein series	2	2	0

Trace form

21 * q - 688084969601007 * q^3 - 800685737036149288416 * q^4 - 36458623571791371420365280 * q^6 - 2702047559314351527601390326 * q^7 + 45992711688628379060241515442429 * q^9 - 783798592344000703899756417518400 * q^10 + 313126982154513861252459017125509792 * q^12 + 7097926243613473019176328483636438706 * q^13 + 291841906843973945390453919652713854400 * q^15 + 40614425652107854809231797245756798419456 * q^16 - 1327598375030727473316959111629621787325120 * q^18 - 3026253719358562084411563912125371924232382 * q^19 + 94405468614025363801741480774192639322611842 * q^21 - 19209253722854761211546865955725969475475520 * q^22 - 8536939678857788536491103872952212579880680960 * q^24 - 17147961692404127551588071265216534139284367475 * q^25 + 386598848155105460060789059338932209496472438297 * q^27 - 996205777307676532598553893751207432016740832704 * q^28 - 13469561117532417280775174235598750536019791067200 * q^30 - 14654619455858594306346020767449979844677242053478 * q^31 + 76031443883614128882573745917963369573166525959360 * q^33 - 607578292754219603165333260413176675880514014447360 * q^34 - 895023811463443645999922679504197455464847252142304 * q^36 + 20017769738379707622473792283398210981888313792060834 * q^37 + 66636801091900395134689625163950363064549067501207818 * q^39 - 164157270356735970397207190518038139497893424374707200 * q^40 - 362475530834094311762041222130355899146344066985844160 * q^42 + 1750683764257600519072611471115188115349321260457464146 * q^43 + 2893961767142107219663835709681578507068881328379222400 * q^45 - 9354105762324374445425328051923657080564209708616152960 * q^46 + 13817528706178021501150679795616158657279365440273074688 * q^48 + 215128591806865673017752231478506065368765042180747979727 * q^49 + 244898096463243383440025305755038369424109352434412094720 * q^51 - 1518265416812062984196689570755057404628632785205545096896 * q^52 - 386962012382976993771518038850875450617071434969909598880 * q^54 + 1313751320608480207642793301222628514163843327983665564800 * q^55 + 19099434894617664662341642357315366358083446634989076587354 * q^57 - 100361163480954821917122043432794223233970822326053950441920 * q^58 + 188095594234899922680776576921513155518384075353356847385600 * q^60 + 113336939225624355656015939981441781500323155005015569459602 * q^61 + 867289963069300891393622628986175964602499204766868854587866 * q^63 - 3834144414815230440260964913649794504762796578058449640349696 * q^64 + 8309681532541455738248790801869091701653966958238676467844800 * q^66 - 6049423726944633447191209261927909749694186597555115893152606 * q^67 + 26395268384310228436148510386607667671115625880708467370286720 * q^69 - 53673269104481250134670425876769459429788829882429608923689600 * q^70 + 135607917285688125946137613885497485690645144416066370695173120 * q^72 - 178147484335790867284195105212850456640968756739384871647383494 * q^73 + 48500659963334295446540398772268295428047679651616767953046825 * q^75 - 149865848814600171328195720360577671384923125006177154868747968 * q^76 + 42333034554100439516880814575759716324771014654582144994836800 * q^78 + 444494431904136800989393001687173188707366949918924051811195578 * q^79 - 1714755033212258332948685465092598786715301424884224614290293339 * q^81 + 9780548955253740491517774427483475844287869484539284101189512320 * q^82 - 23209425572238177028755357107740308790467159790146246204677483712 * q^84 + 15725476767553808561610465539289169056529282358913795578981260800 * q^85 - 20361537149674837364457194316410702650457831770981879709222020800 * q^87 + 43127341602231234631198337877354797375008485566513397535855918080 * q^88 - 68986845993042571618317468832763287342807845905185213796199009600 * q^90 + 3262721652025066881755116254518958419295537752131404627143858724 * q^91 + 165867495181307153265816567053181483924867691908493681948316622546 * q^93 - 243292275786183398644891798798613800120302016678942850492866824960 * q^94 + 1707340756716414995397633331453898170371668874444383803046536028160 * q^96 - 1800313724485416009736937253676448843389370135068996806872381547606 * q^97 + 1311784025950014883691036763145966005164166837426590048709685526400 * q^99

Decomposition of \(S_{67}^{\mathrm{new}}(3, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.67.b.a	$3$	$67$	3.b	3.b	$2$	$1$	$1$	$82.760$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			3.67.b.a	$2$	$0$	\(0\)	\(-55\!\cdots\!23\)	\(0\)	\(-15\!\cdots\!14\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{33}q^{3}+2^{66}q^{4}+\cdots\)
3.67.b.b	$3$	$67$	3.b	3.b	$2$	$20$	$20$	$82.760$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		3.67.b.b	$2$	$0$	\(0\)	\(48\!\cdots\!16\)	\(0\)	\(12\!\cdots\!88\)	$2^{216}\cdot 3^{291}\cdot 5^{20}\cdot 7^{10}\cdot 11^{6}\cdot 13^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(243548779847726+15513\beta _{1}+\cdots)q^{3}+\cdots\)