Properties

Label 63.2.a
Level $63$
Weight $2$
Character orbit 63.a
Rep. character $\chi_{63}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(63))\).

Total New Old
Modular forms 12 3 9
Cusp forms 5 3 2
Eisenstein series 7 0 7

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.
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(3\)

Trace form

\( 3 q + q^{2} + q^{4} + 2 q^{5} + q^{7} - 3 q^{8} + O(q^{10}) \) \( 3 q + q^{2} + q^{4} + 2 q^{5} + q^{7} - 3 q^{8} - 10 q^{10} - 4 q^{11} + 2 q^{13} - q^{14} - 11 q^{16} + 6 q^{17} - 4 q^{19} - 2 q^{20} + 8 q^{22} + 13 q^{25} - 2 q^{26} + 3 q^{28} + 2 q^{29} - 8 q^{31} + 5 q^{32} + 18 q^{34} - 2 q^{35} + 10 q^{37} + 4 q^{38} + 6 q^{40} - 2 q^{41} - 12 q^{43} + 4 q^{44} - 12 q^{46} + 3 q^{49} - q^{50} + 6 q^{52} - 6 q^{53} - 32 q^{55} + 3 q^{56} + 2 q^{58} - 12 q^{59} - 22 q^{61} + 9 q^{64} - 4 q^{65} - 4 q^{67} - 6 q^{68} - 14 q^{70} + 22 q^{73} + 6 q^{74} - 12 q^{76} + 4 q^{77} - 2 q^{80} + 34 q^{82} + 12 q^{83} - 12 q^{85} - 4 q^{86} + 14 q^{89} + 6 q^{91} + 24 q^{94} + 8 q^{95} + 46 q^{97} + q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(63))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7
63.2.a.a \(1\) \(0.503\) \(\Q\) None \(1\) \(0\) \(2\) \(-1\) \(-\) \(+\) \(q+q^{2}-q^{4}+2q^{5}-q^{7}-3q^{8}+2q^{10}+\cdots\)
63.2.a.b \(2\) \(0.503\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(q+\beta q^{2}+q^{4}-2\beta q^{5}+q^{7}-\beta q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(63))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(63)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)