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

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

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(63))\) 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
63.4.a.a 63.a 1.a $1$ $3.717$ \(\Q\) None 21.4.a.b \(-4\) \(0\) \(4\) \(-7\) $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+8q^{4}+4q^{5}-7q^{7}-2^{4}q^{10}+\cdots\)
63.4.a.b 63.a 1.a $1$ $3.717$ \(\Q\) None 7.4.a.a \(1\) \(0\) \(-16\) \(-7\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-7q^{4}-2^{4}q^{5}-7q^{7}-15q^{8}+\cdots\)
63.4.a.c 63.a 1.a $1$ $3.717$ \(\Q\) None 21.4.a.a \(3\) \(0\) \(18\) \(7\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{2}+q^{4}+18q^{5}+7q^{7}-21q^{8}+\cdots\)
63.4.a.d 63.a 1.a $2$ $3.717$ \(\Q(\sqrt{19}) \) None 63.4.a.d \(0\) \(0\) \(0\) \(-14\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+11q^{4}+2\beta q^{5}-7q^{7}+3\beta q^{8}+\cdots\)
63.4.a.e 63.a 1.a $2$ $3.717$ \(\Q(\sqrt{57}) \) None 21.4.a.c \(3\) \(0\) \(-6\) \(14\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(7+3\beta )q^{4}+(-2-2\beta )q^{5}+\cdots\)

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

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