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
Newform subspaces 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: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

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 \(0\) \(-3\) \(0\) \(-56\) \(q+(\beta _{2}-\beta _{6})q^{2}+(\beta _{7}+\beta _{8})q^{3}+(-2\beta _{4}+\cdots)q^{4}+\cdots\)