Properties

Label 21.30.c
Level $21$
Weight $30$
Character orbit 21.c
Rep. character $\chi_{21}(20,\cdot)$
Character field $\Q$
Dimension $76$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 30 \)
Character orbit: \([\chi]\) \(=\) 21.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(21, [\chi])\).

Total New Old
Modular forms 80 80 0
Cusp forms 76 76 0
Eisenstein series 4 4 0

Trace form

\( 76q - 20401094660q^{4} + 1962751543872q^{7} - 89581451225964q^{9} + O(q^{10}) \) \( 76q - 20401094660q^{4} + 1962751543872q^{7} - 89581451225964q^{9} - 116668222909200048q^{15} + 4964525139713333892q^{16} + 1542346202347854996q^{18} + 33840646982361357348q^{21} - 9870996616978150672q^{22} + 3225406746743103424612q^{25} - 3181907581338093199564q^{28} + 5113912044496410095244q^{30} - 85758641407134848258352q^{36} - 17812771227715200149976q^{37} + 388095283792424641491696q^{39} + 804036587819434104664956q^{42} + 2391536152977907871782320q^{43} - 1070985628070611677307000q^{46} - 512656982878691867441540q^{49} - 961431915936904000664400q^{51} + 20345422731681279280765248q^{57} - 40096240109469024574169272q^{58} - 164991837955115951799442596q^{60} - 360764839802574990409097184q^{63} - 1608343949909674725081473028q^{64} + 483978610969894046870693264q^{67} - 656026306765550013508448520q^{70} + 1937172856654554597960695124q^{72} - 8054141680325499868559088636q^{78} - 11740735193468750125742145952q^{79} + 18477545939654446572971367132q^{81} - 7249045143271847568431965452q^{84} + 14576359553686844022629140848q^{85} - 1685535263940707754634995584q^{88} + 44135166284535829618726469040q^{91} + 226499776928895503792863540632q^{93} - 231093384978708762520959066624q^{99} + O(q^{100}) \)

Decomposition of \(S_{30}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
21.30.c.a \(76\) \(111.884\) None \(0\) \(0\) \(0\) \(19\!\cdots\!72\)