Properties

Label 21.4.c
Level 21
Weight 4
Character orbit c
Rep. character \(\chi_{21}(20,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 2
Sturm bound 10
Trace bound 1

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

Trace form

\(6q \) \(\mathstrut -\mathstrut 20q^{4} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 42q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 20q^{4} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 42q^{9} \) \(\mathstrut -\mathstrut 204q^{15} \) \(\mathstrut -\mathstrut 92q^{16} \) \(\mathstrut +\mathstrut 204q^{18} \) \(\mathstrut +\mathstrut 78q^{21} \) \(\mathstrut +\mathstrut 544q^{22} \) \(\mathstrut -\mathstrut 342q^{25} \) \(\mathstrut -\mathstrut 412q^{28} \) \(\mathstrut -\mathstrut 204q^{30} \) \(\mathstrut -\mathstrut 1296q^{36} \) \(\mathstrut +\mathstrut 700q^{37} \) \(\mathstrut +\mathstrut 924q^{39} \) \(\mathstrut +\mathstrut 1428q^{42} \) \(\mathstrut +\mathstrut 1216q^{43} \) \(\mathstrut -\mathstrut 1496q^{46} \) \(\mathstrut -\mathstrut 1266q^{49} \) \(\mathstrut -\mathstrut 1224q^{51} \) \(\mathstrut -\mathstrut 1800q^{57} \) \(\mathstrut +\mathstrut 952q^{58} \) \(\mathstrut +\mathstrut 1836q^{60} \) \(\mathstrut +\mathstrut 1212q^{63} \) \(\mathstrut +\mathstrut 3548q^{64} \) \(\mathstrut -\mathstrut 2016q^{67} \) \(\mathstrut -\mathstrut 2856q^{70} \) \(\mathstrut -\mathstrut 204q^{72} \) \(\mathstrut -\mathstrut 4692q^{78} \) \(\mathstrut +\mathstrut 3150q^{81} \) \(\mathstrut +\mathstrut 2052q^{84} \) \(\mathstrut +\mathstrut 2448q^{85} \) \(\mathstrut -\mathstrut 544q^{88} \) \(\mathstrut +\mathstrut 1920q^{91} \) \(\mathstrut -\mathstrut 372q^{93} \) \(\mathstrut -\mathstrut 1632q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.c.a \(2\) \(1.239\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-20\) \(q-\zeta_{6}q^{3}+8q^{4}+(-10+3\zeta_{6})q^{7}+\cdots\)
21.4.c.b \(4\) \(1.239\) \(\Q(\sqrt{-6}, \sqrt{-17})\) None \(0\) \(0\) \(0\) \(28\) \(q-\beta _{2}q^{2}+\beta _{3}q^{3}-9q^{4}+(-\beta _{1}-2\beta _{3})q^{5}+\cdots\)