Properties

Label 21.33.h
Level $21$
Weight $33$
Character orbit 21.h
Rep. character $\chi_{21}(2,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $166$
Newform subspaces $2$
Sturm bound $88$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 33 \)
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: \(88\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{33}(21, [\chi])\).

Total New Old
Modular forms 174 174 0
Cusp forms 166 166 0
Eisenstein series 8 8 0

Trace form

\( 166q - q^{3} + 171798691838q^{4} + 3915256954876q^{6} + 23283626657033q^{7} - 620299214629855q^{9} + O(q^{10}) \) \( 166q - q^{3} + 171798691838q^{4} + 3915256954876q^{6} + 23283626657033q^{7} - 620299214629855q^{9} - 653609167486978q^{10} - 265168029707289308q^{12} + 1174490826246474670q^{13} + 295985739739384604q^{15} - 369660002185822773514q^{16} - 285770686590685125284q^{18} - 546922388448912176471q^{19} - 2532234138966045352166q^{21} - 13078660526142101830996q^{22} + 1054771135641021243846q^{24} + 355995021793216230445619q^{25} - 300858790784549562824254q^{27} + 290520957821873648162602q^{28} - 330476454165111001470380q^{30} + 1936470604685723886426939q^{31} - 737341781484411371012926q^{33} - 22734196551602082026029296q^{34} - 42849085098001864377018668q^{36} + 16805015137848500313759621q^{37} + 75561307465619785766649701q^{39} - 45599856935659274405824326q^{40} + 104404775512846755306420578q^{42} - 279709081697146614502787074q^{43} + 887905841124226250439410180q^{45} + 30894373905902163402233292q^{46} - 9148859974438891485234987128q^{48} + 2458303555516221952922886469q^{49} + 899880507546787686922713816q^{51} + 3471683216351777250513670640q^{52} + 16340214733829489950275617278q^{54} + 55802929352612492566892052700q^{55} - 9513302389417287709345244242q^{57} + 63615010561534481972086105634q^{58} + 69166368254932319844426127510q^{60} - 10379395267883421634675945622q^{61} - 678824307397998548190412973q^{63} - 1603732050087206969297742306452q^{64} + 207476465882475740955061495384q^{66} + 408150666969189239305352437177q^{67} - 545951930206529644734851269368q^{69} - 186949681822956281680810374050q^{70} + 888211654697324693108978108112q^{72} + 633812229130625576653182883761q^{73} - 2326443392974654489220795728049q^{75} - 14061747746511733816011962014024q^{76} - 15447296386674612875575362375320q^{78} - 907506630728797215404959971541q^{79} + 750123451429134021774437836217q^{81} - 1761459771487793738918439695372q^{82} + 19778104845600691516206381522968q^{84} - 11022683040979827410048301708864q^{85} + 25044534894104609383997596533098q^{87} - 10870298495939867424336956818290q^{88} - 139965199147883927707395151444364q^{90} + 41898882097126373291950265106485q^{91} - 27788314570397186691018573550827q^{93} - 96599767300412991404126578997724q^{94} + 140734633946824944269642969435810q^{96} - 21027210205848943233065360945496q^{97} - 241354569337789054930139182218232q^{99} + O(q^{100}) \)

Decomposition of \(S_{33}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
21.33.h.a \(2\) \(136.220\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-43046721\) \(0\) \(65\!\cdots\!59\) \(q-3^{16}\zeta_{6}q^{3}-2^{32}\zeta_{6}q^{4}+(36372171914815+\cdots)q^{7}+\cdots\)
21.33.h.b \(164\) \(136.220\) None \(0\) \(43046720\) \(0\) \(-4\!\cdots\!26\)