Space of modular forms of level 4, weight 45, and Character 4.b

• Label: 4.45.b
• Level: $4$
• Weight: $45$
• Character orbit: 4.b
• Rep. character: $\chi_{4}(3,\cdot)$
• Character field: $\Q$
• Dimension: $21$
• Newform subspaces: $2$
• Sturm bound: $22$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 45 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(22\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{45}(4, [\chi])\).

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

Trace form

21 * q + 605612 * q^2 - 13046580445680 * q^4 - 1191857871142214 * q^5 - 151089021270839424 * q^6 + 96298933068226423232 * q^8 - 5759619100948009102011 * q^9 - 12505573328866519603944 * q^10 - 1008582008803903346004480 * q^12 - 342266720642595008327526 * q^13 - 18812570969221737757007616 * q^14 - 429323192915437820302089984 * q^16 - 634801063423464784179430166 * q^17 - 3038124069658099834390851348 * q^18 - 95178771568328392075054272224 * q^20 + 25941411600333949914183048192 * q^21 + 727384969503500811258425746560 * q^22 - 6784766426651218183744450246656 * q^24 + 22093991393233408379523436028271 * q^25 + 53422584580753843254877931773336 * q^26 - 46674441078105565706123745254400 * q^28 - 172856649054100027513483366649510 * q^29 - 208471390136203333591535590099200 * q^30 + 3242792133809678876696622531894272 * q^32 + 7273361532485316304507716956536320 * q^33 - 13156262381829636429055579069468584 * q^34 - 33874660869572147385235178078305008 * q^36 - 16356933662060836651930347592620486 * q^37 + 45856687255867991685965015678509440 * q^38 - 483040727182327173950693008664191104 * q^40 + 211290721897052900032957839223418122 * q^41 + 409589852913664867740496861674209280 * q^42 + 3339472512955444037822475478956188160 * q^44 + 2039093001210970787360916299316874266 * q^45 - 5806749290972389592256524077295633664 * q^46 - 5340253533684189604832993455433195520 * q^48 - 43299262012369466157823154150393550411 * q^49 + 28288224613316806931187340605385090116 * q^50 - 109456821928895615986497840386233526496 * q^52 - 124060719819939466178716849900255596806 * q^53 + 85603264604984031892020748836682460928 * q^54 + 311261017039966191188280314622394331136 * q^56 + 406929883110207715079424916765543918080 * q^57 - 2126008932920829662698391859008777819496 * q^58 - 372686235229043362754072188852707148800 * q^60 + 309426872572239588043263812927207839962 * q^61 + 1156322127848885203066778833646710993920 * q^62 - 4902730151741626597806839009324881735680 * q^64 - 13492158093033658477402057894275487889068 * q^65 + 24932659300030021765520575242010626293760 * q^66 - 3916274595737468444125500208547201271776 * q^68 + 2565337248483798670232893328361624695808 * q^69 - 98879252613169806434542823461625902886400 * q^70 + 147302554284819254485927378700631841025472 * q^72 + 147531457140172751132283617562594502945674 * q^73 + 290171560916431669411259551792076861277976 * q^74 - 43184981979196571535874879172681105164800 * q^76 + 446394181490740211970215422489995719377920 * q^77 - 964200119976088262334169600001693579520 * q^78 - 2011490663947381735501612576922685486493184 * q^80 - 2178726246184026497923052568920748979977867 * q^81 - 1150958323935947560362508440440048448874536 * q^82 + 6209941380868192540343252076606108902719488 * q^84 + 5679851477841926148420178187348291823631092 * q^85 - 2915338479242605399415746860762643287652224 * q^86 + 705030880368125854811890748326710823188480 * q^88 - 27170409944693321104174610773080947078942390 * q^89 + 12369354273355664792550176907847193877155736 * q^90 - 27540241567678746217506869357458705431966720 * q^92 + 41096485388187686620928799812891400047800320 * q^93 + 15862476520232897460465561775346899863780864 * q^94 - 34622322558806891728108279325640392329887744 * q^96 - 108718469585945280803765850286496694817884246 * q^97 - 102805093097570330181433576830227627173185748 * q^98

Decomposition of \(S_{45}^{\mathrm{new}}(4, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4.45.b.a	$4$	$45$	4.b	4.b	$2$	$1$	$1$	$49.048$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	✓			4.45.b.a	$2$	$0$	\(-4194304\)	\(0\)	\(94\!\cdots\!86\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{22}q^{2}+2^{44}q^{4}+94681488501586q^{5}+\cdots\)
4.45.b.b	$4$	$45$	4.b	4.b	$2$	$20$	$20$	$49.048$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		4.45.b.b	$2$	$0$	\(4799916\)	\(0\)	\(-12\!\cdots\!00\)	\(0\)	$2^{380}\cdot 3^{44}\cdot 5^{12}\cdot 7^{2}\cdot 11^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(239996+\beta _{1})q^{2}+(86+431\beta _{1}+\cdots)q^{3}+\cdots\)