Properties

Label 21.4.a
Level $21$
Weight $4$
Character orbit 21.a
Rep. character $\chi_{21}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $10$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 21.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(10\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(21))\).

Total New Old
Modular forms 10 4 6
Cusp forms 6 4 2
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(1\)

Trace form

\( 4q - 2q^{2} + 26q^{4} - 16q^{5} - 12q^{6} + 14q^{7} - 66q^{8} + 36q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 26q^{4} - 16q^{5} - 12q^{6} + 14q^{7} - 66q^{8} + 36q^{9} - 28q^{10} + 20q^{11} + 24q^{12} - 80q^{13} - 70q^{14} + 84q^{15} + 2q^{16} + 120q^{17} - 18q^{18} + 40q^{19} + 172q^{20} + 42q^{21} + 80q^{22} - 36q^{23} - 324q^{24} - 28q^{25} + 172q^{26} + 70q^{28} - 160q^{29} - 312q^{30} - 168q^{31} - 490q^{32} - 96q^{33} + 276q^{34} - 56q^{35} + 234q^{36} - 96q^{37} + 1360q^{38} + 336q^{39} - 924q^{40} - 1016q^{41} + 84q^{42} + 176q^{43} + 1264q^{44} - 144q^{45} + 792q^{46} + 552q^{47} + 816q^{48} + 196q^{49} - 1198q^{50} - 396q^{51} - 1420q^{52} - 1344q^{53} - 108q^{54} + 952q^{55} - 462q^{56} + 264q^{57} - 652q^{58} + 792q^{59} + 816q^{60} + 592q^{61} - 1824q^{62} + 126q^{63} + 1210q^{64} + 224q^{65} - 1896q^{66} + 1144q^{67} + 492q^{68} + 144q^{69} + 28q^{70} - 444q^{71} - 594q^{72} - 72q^{73} - 780q^{74} - 624q^{75} - 832q^{76} - 728q^{77} + 1392q^{78} - 856q^{79} + 3484q^{80} + 324q^{81} + 1492q^{82} + 2208q^{83} + 504q^{84} - 1224q^{85} + 1880q^{86} - 1032q^{87} - 1920q^{88} + 920q^{89} - 252q^{90} + 308q^{91} - 3192q^{92} + 744q^{93} - 1344q^{94} + 656q^{95} - 204q^{96} - 744q^{97} - 98q^{98} + 180q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(21))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7
21.4.a.a \(1\) \(1.239\) \(\Q\) None \(-3\) \(-3\) \(-18\) \(7\) \(+\) \(-\) \(q-3q^{2}-3q^{3}+q^{4}-18q^{5}+9q^{6}+\cdots\)
21.4.a.b \(1\) \(1.239\) \(\Q\) None \(4\) \(-3\) \(-4\) \(-7\) \(+\) \(+\) \(q+4q^{2}-3q^{3}+8q^{4}-4q^{5}-12q^{6}+\cdots\)
21.4.a.c \(2\) \(1.239\) \(\Q(\sqrt{57}) \) None \(-3\) \(6\) \(6\) \(14\) \(-\) \(-\) \(q+(-1-\beta )q^{2}+3q^{3}+(7+3\beta )q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(21))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(21)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)