Properties

Label 21.6.e
Level $21$
Weight $6$
Character orbit 21.e
Rep. character $\chi_{21}(4,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $14$
Newform subspaces $3$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 21.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(21, [\chi])\).

Total New Old
Modular forms 30 14 16
Cusp forms 22 14 8
Eisenstein series 8 0 8

Trace form

\( 14q + 2q^{2} - 9q^{3} - 106q^{4} + 22q^{5} + 144q^{6} + 167q^{7} - 264q^{8} - 567q^{9} + O(q^{10}) \) \( 14q + 2q^{2} - 9q^{3} - 106q^{4} + 22q^{5} + 144q^{6} + 167q^{7} - 264q^{8} - 567q^{9} - 1182q^{10} + 466q^{11} - 288q^{12} + 2158q^{13} + 4558q^{14} + 396q^{15} - 3034q^{16} - 1848q^{17} + 162q^{18} - 2657q^{19} + 1448q^{20} - 4068q^{21} + 4836q^{22} - 5232q^{23} - 3402q^{24} - 205q^{25} + 17030q^{26} + 1458q^{27} - 9358q^{28} + 1480q^{29} + 5544q^{30} - 725q^{31} - 11384q^{32} - 11430q^{33} - 1176q^{34} - 19234q^{35} + 17172q^{36} + 15187q^{37} + 47750q^{38} + 1395q^{39} - 3318q^{40} - 50812q^{41} - 16344q^{42} + 37066q^{43} - 26632q^{44} + 1782q^{45} - 27588q^{46} + 17118q^{47} + 63216q^{48} - 36763q^{49} - 61292q^{50} + 11664q^{51} + 5428q^{52} + 47652q^{53} - 5832q^{54} + 187944q^{55} + 80784q^{56} - 29466q^{57} - 45198q^{58} - 67764q^{59} - 78426q^{60} - 51854q^{61} - 183420q^{62} + 14013q^{63} - 228412q^{64} - 40370q^{65} - 2988q^{66} + 7309q^{67} + 66612q^{68} + 154224q^{69} + 149490q^{70} + 306180q^{71} + 10692q^{72} - 65927q^{73} + 240570q^{74} - 48807q^{75} + 222184q^{76} - 204544q^{77} - 238428q^{78} + 48997q^{79} + 97676q^{80} - 45927q^{81} - 5268q^{82} - 430740q^{83} + 47160q^{84} - 132912q^{85} - 137330q^{86} - 3060q^{87} - 332442q^{88} + 163120q^{89} + 191484q^{90} - 136925q^{91} + 833112q^{92} + 121905q^{93} + 5988q^{94} + 284842q^{95} - 176886q^{96} - 86924q^{97} - 40636q^{98} - 75492q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
21.6.e.a \(2\) \(3.368\) \(\Q(\sqrt{-3}) \) None \(2\) \(9\) \(-11\) \(259\) \(q+(2-2\zeta_{6})q^{2}+9\zeta_{6}q^{3}+28\zeta_{6}q^{4}+\cdots\)
21.6.e.b \(4\) \(3.368\) \(\Q(\sqrt{-3}, \sqrt{-83})\) None \(3\) \(18\) \(33\) \(-350\) \(q+(1+\beta _{1}-\beta _{3})q^{2}-9\beta _{1}q^{3}+(31\beta _{1}+\cdots)q^{4}+\cdots\)
21.6.e.c \(8\) \(3.368\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-3\) \(-36\) \(0\) \(258\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+9\beta _{2}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(21, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)