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Properties

Label 21.4.e
Level $21$
Weight $4$
Character orbit 21.e
Rep. character $\chi_{21}(4,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $2$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
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 20 8 12
Cusp forms 12 8 4
Eisenstein series 8 0 8

Trace form

\( 8q + 2q^{2} + 6q^{3} - 26q^{4} - 8q^{5} - 24q^{6} - 20q^{7} + 120q^{8} - 36q^{9} + O(q^{10}) \) \( 8q + 2q^{2} + 6q^{3} - 26q^{4} - 8q^{5} - 24q^{6} - 20q^{7} + 120q^{8} - 36q^{9} + 46q^{10} - 20q^{11} + 72q^{12} - 4q^{13} - 242q^{14} - 84q^{15} - 170q^{16} - 132q^{17} + 18q^{18} + 218q^{19} + 872q^{20} + 108q^{21} + 76q^{22} - 132q^{23} + 54q^{24} - 14q^{25} - 466q^{26} - 108q^{27} - 166q^{28} - 488q^{29} - 192q^{30} + 348q^{31} - 728q^{32} + 150q^{33} - 552q^{34} + 140q^{35} + 468q^{36} + 54q^{37} + 350q^{38} + 378q^{39} + 42q^{40} + 1208q^{41} - 156q^{42} + 772q^{43} + 920q^{44} - 72q^{45} + 804q^{46} + 240q^{47} - 1872q^{48} - 940q^{49} - 2060q^{50} - 108q^{51} - 260q^{52} - 756q^{53} + 108q^{54} - 1972q^{55} + 1152q^{56} + 1116q^{57} + 358q^{58} - 1128q^{59} + 1326q^{60} + 188q^{61} + 3636q^{62} - 126q^{63} + 68q^{64} + 280q^{65} - 156q^{66} + 998q^{67} - 2028q^{68} - 1800q^{69} + 3566q^{70} - 48q^{71} - 540q^{72} - 1350q^{73} - 1950q^{74} + 738q^{75} - 4712q^{76} + 548q^{77} - 492q^{78} - 1328q^{79} - 388q^{80} - 324q^{81} + 956q^{82} + 1992q^{83} + 1536q^{84} + 3096q^{85} + 3286q^{86} + 1050q^{87} + 1206q^{88} - 2672q^{89} - 828q^{90} - 206q^{91} - 1512q^{92} + 474q^{93} + 3204q^{94} + 688q^{95} + 1914q^{96} + 1044q^{97} - 5884q^{98} + 360q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.e.a \(2\) \(1.239\) \(\Q(\sqrt{-3}) \) None \(3\) \(-3\) \(3\) \(-7\) \(q+(3-3\zeta_{6})q^{2}-3\zeta_{6}q^{3}-\zeta_{6}q^{4}+(3+\cdots)q^{5}+\cdots\)
21.4.e.b \(6\) \(1.239\) 6.0.9924270768.1 None \(-1\) \(9\) \(-11\) \(-13\) \(q-\beta _{1}q^{2}+(3-3\beta _{4})q^{3}+(-8+\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(21, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)