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Properties

Label 21.29.h
Level $21$
Weight $29$
Character orbit 21.h
Rep. character $\chi_{21}(2,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $146$
Newform subspaces $2$
Sturm bound $77$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 29 \)
Character orbit: \([\chi]\) \(=\) 21.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(77\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{29}(21, [\chi])\).

Total New Old
Modular forms 154 154 0
Cusp forms 146 146 0
Eisenstein series 8 8 0

Trace form

\( 146 q - q^{3} + 9663676414 q^{4} - 100254613508 q^{6} + 1095434973823 q^{7} + 35923285076813 q^{9} + O(q^{10}) \) \( 146 q - q^{3} + 9663676414 q^{4} - 100254613508 q^{6} + 1095434973823 q^{7} + 35923285076813 q^{9} - 25885338894338 q^{10} - 1437433635884108 q^{12} - 8252304558985870 q^{13} - 60581246761142776 q^{15} - 1313207164051739402 q^{16} + 5866562793163516 q^{18} + 1771850015797165307 q^{19} + 4207153361263379164 q^{21} + 1959274357328345644 q^{22} - 2500469745196614282 q^{24} + 443646314271319232269 q^{25} + 277608338073736873526 q^{27} - 763020587505375067798 q^{28} - 1037340185283073362620 q^{30} + 1573030170093041449137 q^{31} + 1457302107578995298264 q^{33} + 15555745834757524689552 q^{34} + 29700644075933661165460 q^{36} - 9134205456366413432049 q^{37} - 2737554612191926398745 q^{39} - 76812305934969191520486 q^{40} - 614898149845189655662 q^{42} + 109009940417488596702466 q^{43} - 233445440221705289154850 q^{45} - 988410838215082535589204 q^{46} + 76514584542653921519752 q^{48} - 506041138571893656158797 q^{49} + 81472852686494106097938 q^{51} + 1033078468551541868273200 q^{52} - 6464826892154265915045458 q^{54} - 4704365025957970444893220 q^{55} + 6772026558378808568123438 q^{57} - 12585639508229034555408926 q^{58} - 17649777084418026550246490 q^{60} + 7313980014613021035896018 q^{61} - 4540485025338286385819933 q^{63} - 210096195503612563555774036 q^{64} - 68006037955706011046711000 q^{66} + 13341006173232442126197707 q^{67} + 15483902557784731685166636 q^{69} - 371939592317373720306804130 q^{70} - 95320201105622777556980448 q^{72} - 298078027997437221420217389 q^{73} + 442442505868325522094618781 q^{75} + 1581964694625860805385569208 q^{76} - 806497062567498204270408440 q^{78} + 141839804384454479965508737 q^{79} - 397897918063684624841720419 q^{81} - 3485188024224928821104054092 q^{82} + 6848480150657226620586648056 q^{84} + 6184574282291538285489924936 q^{85} - 594392062478485254939548362 q^{87} + 3880843260464666211147844110 q^{88} + 2276268870376382767790273236 q^{90} - 5473542142212065386512555821 q^{91} - 1136405168994382038098612787 q^{93} - 10538535892519794493877406108 q^{94} + 37984063050009106702623481250 q^{96} - 4379418740056881568510576776 q^{97} - 53298269295060781334719315300 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{29}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.29.h.a 21.h 21.h $2$ $104.304$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-4782969\) \(0\) \(778317387191\) $\mathrm{U}(1)[D_{6}]$ \(q-3^{14}\zeta_{6}q^{3}-2^{28}\zeta_{6}q^{4}+(68460472135+\cdots)q^{7}+\cdots\)
21.29.h.b 21.h 21.h $144$ $104.304$ None \(0\) \(4782968\) \(0\) \(317117586632\) $\mathrm{SU}(2)[C_{6}]$