Properties

Label 63.4.a
Level $63$
Weight $4$
Character orbit 63.a
Rep. character $\chi_{63}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $5$
Sturm bound $32$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(32\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(63))\).

Total New Old
Modular forms 28 7 21
Cusp forms 20 7 13
Eisenstein series 8 0 8

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.
\(+\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(5\)
Minus space\(-\)\(2\)

Trace form

\( 7q + 3q^{2} + 41q^{4} - 7q^{7} + 51q^{8} + O(q^{10}) \) \( 7q + 3q^{2} + 41q^{4} - 7q^{7} + 51q^{8} + 32q^{10} - 12q^{11} + 112q^{13} + 63q^{14} - 19q^{16} - 174q^{17} - 110q^{19} - 60q^{20} - 292q^{22} - 12q^{23} + 5q^{25} - 144q^{26} - 35q^{28} + 270q^{29} + 156q^{31} + 651q^{32} - 462q^{34} + 168q^{35} + 30q^{37} - 1470q^{38} - 456q^{40} + 834q^{41} + 632q^{43} - 1320q^{44} - 396q^{46} - 876q^{47} + 343q^{49} + 1329q^{50} + 188q^{52} + 1506q^{53} + 64q^{55} + 567q^{56} + 1586q^{58} - 1602q^{59} + 1684q^{61} + 1836q^{62} - 551q^{64} - 672q^{65} + 1300q^{67} - 114q^{68} - 392q^{70} + 1212q^{71} - 522q^{73} + 534q^{74} - 502q^{76} + 672q^{77} - 1840q^{79} - 4140q^{80} - 134q^{82} - 906q^{83} - 1728q^{85} - 1752q^{86} - 3180q^{88} - 1650q^{89} - 1036q^{91} + 3528q^{92} + 2436q^{94} + 1104q^{95} + 1146q^{97} + 147q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(63))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7
63.4.a.a \(1\) \(3.717\) \(\Q\) None \(-4\) \(0\) \(4\) \(-7\) \(-\) \(+\) \(q-4q^{2}+8q^{4}+4q^{5}-7q^{7}-2^{4}q^{10}+\cdots\)
63.4.a.b \(1\) \(3.717\) \(\Q\) None \(1\) \(0\) \(-16\) \(-7\) \(-\) \(+\) \(q+q^{2}-7q^{4}-2^{4}q^{5}-7q^{7}-15q^{8}+\cdots\)
63.4.a.c \(1\) \(3.717\) \(\Q\) None \(3\) \(0\) \(18\) \(7\) \(-\) \(-\) \(q+3q^{2}+q^{4}+18q^{5}+7q^{7}-21q^{8}+\cdots\)
63.4.a.d \(2\) \(3.717\) \(\Q(\sqrt{19}) \) None \(0\) \(0\) \(0\) \(-14\) \(+\) \(+\) \(q+\beta q^{2}+11q^{4}+2\beta q^{5}-7q^{7}+3\beta q^{8}+\cdots\)
63.4.a.e \(2\) \(3.717\) \(\Q(\sqrt{57}) \) None \(3\) \(0\) \(-6\) \(14\) \(-\) \(-\) \(q+(1+\beta )q^{2}+(7+3\beta )q^{4}+(-2-2\beta )q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(63))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(63)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)