Properties

Label 21.2.a
Level 21
Weight 2
Character orbit a
Rep. character \(\chi_{21}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 21.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(21))\).

Total New Old
Modular forms 4 1 3
Cusp forms 1 1 0
Eisenstein series 3 0 3

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.
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q - q^{2} + q^{3} - q^{4} - 2q^{5} - q^{6} - q^{7} + 3q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} - q^{4} - 2q^{5} - q^{6} - q^{7} + 3q^{8} + q^{9} + 2q^{10} + 4q^{11} - q^{12} - 2q^{13} + q^{14} - 2q^{15} - q^{16} - 6q^{17} - q^{18} + 4q^{19} + 2q^{20} - q^{21} - 4q^{22} + 3q^{24} - q^{25} + 2q^{26} + q^{27} + q^{28} - 2q^{29} + 2q^{30} - 5q^{32} + 4q^{33} + 6q^{34} + 2q^{35} - q^{36} + 6q^{37} - 4q^{38} - 2q^{39} - 6q^{40} + 2q^{41} + q^{42} - 4q^{43} - 4q^{44} - 2q^{45} - q^{48} + q^{49} + q^{50} - 6q^{51} + 2q^{52} + 6q^{53} - q^{54} - 8q^{55} - 3q^{56} + 4q^{57} + 2q^{58} + 12q^{59} + 2q^{60} - 2q^{61} - q^{63} + 7q^{64} + 4q^{65} - 4q^{66} + 4q^{67} + 6q^{68} - 2q^{70} + 3q^{72} - 6q^{73} - 6q^{74} - q^{75} - 4q^{76} - 4q^{77} + 2q^{78} - 16q^{79} + 2q^{80} + q^{81} - 2q^{82} - 12q^{83} + q^{84} + 12q^{85} + 4q^{86} - 2q^{87} + 12q^{88} - 14q^{89} + 2q^{90} + 2q^{91} - 8q^{95} - 5q^{96} + 18q^{97} - q^{98} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7
21.2.a.a \(1\) \(0.168\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) \(-\) \(+\) \(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)