Properties

Label 21.16.c
Level $21$
Weight $16$
Character orbit 21.c
Rep. character $\chi_{21}(20,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $2$
Sturm bound $42$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 16 \)
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: \(42\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(21, [\chi])\).

Total New Old
Modular forms 42 42 0
Cusp forms 38 38 0
Eisenstein series 4 4 0

Trace form

\( 38 q - 589828 q^{4} + 1050960 q^{7} - 6565782 q^{9} + O(q^{10}) \) \( 38 q - 589828 q^{4} + 1050960 q^{7} - 6565782 q^{9} + 648423876 q^{15} + 9248541060 q^{16} + 4297211700 q^{18} + 20225343174 q^{21} + 19454632432 q^{22} + 230833721978 q^{25} - 142707646892 q^{28} - 365532566964 q^{30} + 805812093936 q^{36} + 694646505996 q^{37} - 2199783687204 q^{39} + 7360068918300 q^{42} + 6929191124400 q^{43} + 16687566156712 q^{46} + 231279346670 q^{49} + 33962207399496 q^{51} - 39323485129176 q^{57} - 133150592961176 q^{58} - 82873723039524 q^{60} + 2274461599236 q^{63} - 59580287959812 q^{64} + 83067268386832 q^{67} - 130642951598376 q^{70} - 180301719210828 q^{72} + 169985312791620 q^{78} + 918434825155024 q^{79} + 745465985608590 q^{81} - 374202264186540 q^{84} - 278796091882752 q^{85} - 1648167121319968 q^{88} + 1199181919670016 q^{91} + 435168341426508 q^{93} + 221578250928288 q^{99} + O(q^{100}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.16.c.a 21.c 21.c $2$ $29.966$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1244900\) $\mathrm{U}(1)[D_{2}]$ \(q-3^{5}\zeta_{6}q^{3}+2^{15}q^{4}+(-622450+\cdots)q^{7}+\cdots\)
21.16.c.b 21.c 21.c $36$ $29.966$ None \(0\) \(0\) \(0\) \(2295860\) $\mathrm{SU}(2)[C_{2}]$