Properties

Label 21.22.c
Level $21$
Weight $22$
Character orbit 21.c
Rep. character $\chi_{21}(20,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $2$
Sturm bound $58$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 21.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(58\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(21, [\chi])\).

Total New Old
Modular forms 58 58 0
Cusp forms 54 54 0
Eisenstein series 4 4 0

Trace form

\( 54q - 54525956q^{4} + 298304168q^{7} - 10770061710q^{9} + O(q^{10}) \) \( 54q - 54525956q^{4} + 298304168q^{7} - 10770061710q^{9} - 687153165468q^{15} + 45037875412612q^{16} + 36759093002772q^{18} - 21361304207298q^{21} + 228880341648112q^{22} + 3548494642823562q^{25} - 2685628339220812q^{28} - 2422487119598196q^{30} + 50795822386155600q^{36} + 4299402242744668q^{37} - 9657429075015348q^{39} - 125754675449474820q^{42} + 277691869261125616q^{43} - 1124214920076830456q^{46} + 906809781130583982q^{49} + 4341973540932052200q^{51} - 4914506248901334432q^{57} - 10814528487339424568q^{58} + 13643758017961015644q^{60} - 26425051438882828836q^{63} - 12033810960284129284q^{64} - 11658587217124746000q^{67} + 73727169165159410040q^{70} + 39846964674222889428q^{72} + 45848199464273536260q^{78} + 535346775587250893472q^{79} + 454337585225870025006q^{81} - 585257506869205373580q^{84} - 570842672309470848672q^{85} - 1060053674241923431168q^{88} - 13967188170478076112q^{91} - 3089212290687116419284q^{93} + 1525182290356701596928q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
21.22.c.a \(2\) \(58.690\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1123983020\) \(q+3^{8}\zeta_{6}q^{3}+2^{21}q^{4}+(-561991510+\cdots)q^{7}+\cdots\)
21.22.c.b \(52\) \(58.690\) None \(0\) \(0\) \(0\) \(1422287188\)