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Properties

Label 21.39.d
Level $21$
Weight $39$
Character orbit 21.d
Rep. character $\chi_{21}(13,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $1$
Sturm bound $104$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 39 \)
Character orbit: \([\chi]\) \(=\) 21.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(104\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{39}(21, [\chi])\).

Total New Old
Modular forms 104 50 54
Cusp forms 100 50 50
Eisenstein series 4 0 4

Trace form

\( 50 q + 728458 q^{2} + 6295949268570 q^{4} + 24755972764560074 q^{7} - 5236783868298550 q^{8} - 22514195294549868150 q^{9} + O(q^{10}) \) \( 50 q + 728458 q^{2} + 6295949268570 q^{4} + 24755972764560074 q^{7} - 5236783868298550 q^{8} - 22514195294549868150 q^{9} + 172737739255663025332 q^{11} - 18773602396693451508206 q^{14} + 28052731020666810506184 q^{15} + 1001020288696213368450226 q^{16} - 328012913517544157056254 q^{18} - 8280596185337214590602320 q^{21} + 54881152075021823747129612 q^{22} + 93126732861673377732191428 q^{23} - 3281643846406082262452696206 q^{25} + 21017132984948315655024080322 q^{28} + 7408580372587760643788450260 q^{29} - 31366206849621984259156348176 q^{30} - 130183123031891014083241562022 q^{32} + 471686887447205111547578155056 q^{35} - 2834964627943267561727648780910 q^{36} - 1267205526379446981486364368476 q^{37} - 1392135427096381389727578445560 q^{39} - 14839207412570738734804636590504 q^{42} - 41770137241549647792230776158716 q^{43} + 113732679400531900915428779222436 q^{44} - 130818684625870907876320490096116 q^{46} + 58502818660490405254925097423362 q^{49} - 472721711699679474287124316287206 q^{50} + 431746825180087212170261360067792 q^{51} + 1772321361676643363234231140267156 q^{53} - 7900883877541918153874615330358982 q^{56} + 1869534466682945839179852186614232 q^{57} + 25539835446180499842408696023360804 q^{58} + 22225882846628455484988749016435048 q^{60} - 11147216110557262179531815789084862 q^{63} - 41846596662502786831694341297122478 q^{64} + 142186457679713317062515303722079616 q^{65} - 20420686765981206658223995115860604 q^{67} - 248037171058856915507341774158214584 q^{70} - 34851274650151544124362361842454332 q^{71} + 2358039494524437417092697346723650 q^{72} - 187123610111524324302009367169599804 q^{74} - 173872485589824838305150234037521932 q^{77} + 708317962809481453241939233912814232 q^{78} - 2882622054870786704718773444569324844 q^{79} + 10137779795222628485328066543647688450 q^{81} - 3464619014420127430988712436507652352 q^{84} - 1772192609847582017149044860051643120 q^{85} + 39345113882453955501804102577998738164 q^{86} - 8195372385292256995026193502414421356 q^{88} + 7088702426252666942283851188975929120 q^{91} + 15155246939734922475045429545367474996 q^{92} - 25968948355266196378708205803851982848 q^{93} + 240676453957463185511084346058427966592 q^{95} - 32088573914357701878364980577522114070 q^{98} - 77781023926820610577984219847414199516 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{39}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.39.d.a 21.d 7.b $50$ $192.073$ None \(728458\) \(0\) \(0\) \(24\!\cdots\!74\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{39}^{\mathrm{old}}(21, [\chi])\) into lower level spaces

\( S_{39}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{39}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)