Properties

Label 21.4.g
Level 21
Weight 4
Character orbit g
Rep. character \(\chi_{21}(5,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 12
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 21.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(21, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

Trace form

\(12q \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 14q^{4} \) \(\mathstrut -\mathstrut 56q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 14q^{4} \) \(\mathstrut -\mathstrut 56q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 30q^{10} \) \(\mathstrut -\mathstrut 192q^{12} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 134q^{16} \) \(\mathstrut +\mathstrut 66q^{18} \) \(\mathstrut +\mathstrut 300q^{19} \) \(\mathstrut +\mathstrut 357q^{21} \) \(\mathstrut -\mathstrut 268q^{22} \) \(\mathstrut +\mathstrut 414q^{24} \) \(\mathstrut -\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 602q^{28} \) \(\mathstrut -\mathstrut 822q^{30} \) \(\mathstrut -\mathstrut 930q^{31} \) \(\mathstrut -\mathstrut 855q^{33} \) \(\mathstrut +\mathstrut 852q^{36} \) \(\mathstrut +\mathstrut 764q^{37} \) \(\mathstrut -\mathstrut 426q^{39} \) \(\mathstrut +\mathstrut 2298q^{40} \) \(\mathstrut +\mathstrut 966q^{42} \) \(\mathstrut -\mathstrut 1012q^{43} \) \(\mathstrut +\mathstrut 2367q^{45} \) \(\mathstrut +\mathstrut 608q^{46} \) \(\mathstrut -\mathstrut 336q^{49} \) \(\mathstrut -\mathstrut 1341q^{51} \) \(\mathstrut -\mathstrut 3000q^{52} \) \(\mathstrut -\mathstrut 4158q^{54} \) \(\mathstrut +\mathstrut 270q^{57} \) \(\mathstrut +\mathstrut 2870q^{58} \) \(\mathstrut -\mathstrut 918q^{60} \) \(\mathstrut +\mathstrut 2358q^{61} \) \(\mathstrut +\mathstrut 1071q^{63} \) \(\mathstrut -\mathstrut 548q^{64} \) \(\mathstrut +\mathstrut 2934q^{66} \) \(\mathstrut +\mathstrut 792q^{67} \) \(\mathstrut -\mathstrut 4242q^{70} \) \(\mathstrut -\mathstrut 2712q^{72} \) \(\mathstrut -\mathstrut 2904q^{73} \) \(\mathstrut -\mathstrut 2418q^{75} \) \(\mathstrut +\mathstrut 4296q^{78} \) \(\mathstrut +\mathstrut 1674q^{79} \) \(\mathstrut +\mathstrut 837q^{81} \) \(\mathstrut +\mathstrut 5040q^{82} \) \(\mathstrut +\mathstrut 3864q^{84} \) \(\mathstrut +\mathstrut 348q^{85} \) \(\mathstrut +\mathstrut 1638q^{87} \) \(\mathstrut -\mathstrut 554q^{88} \) \(\mathstrut -\mathstrut 1218q^{91} \) \(\mathstrut -\mathstrut 1479q^{93} \) \(\mathstrut -\mathstrut 1356q^{94} \) \(\mathstrut -\mathstrut 4410q^{96} \) \(\mathstrut -\mathstrut 3354q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(21, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
21.4.g.a \(12\) \(1.239\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-3\) \(0\) \(-56\) \(q+(\beta _{2}-\beta _{6})q^{2}+(\beta _{7}+\beta _{8})q^{3}+(-2\beta _{4}+\cdots)q^{4}+\cdots\)