Properties

Label 21.2.a
Level $21$
Weight $2$
Character orbit 21.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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7
21.2.a.a 21.a 1.a $1$ $0.168$ \(\Q\) None 21.2.a.a \(-1\) \(1\) \(-2\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)