↑

Properties

Label 63.3.m
Level $63$
Weight $3$
Character orbit 63.m
Rep. character $\chi_{63}(10,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $5$
Sturm bound $24$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 63.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(63, [\chi])\).

Total New Old
Modular forms 40 16 24
Cusp forms 24 12 12
Eisenstein series 16 4 12

Trace form

\( 12 q + 2 q^{2} - 16 q^{4} + 6 q^{5} - 14 q^{7} - 8 q^{8} + O(q^{10}) \) \( 12 q + 2 q^{2} - 16 q^{4} + 6 q^{5} - 14 q^{7} - 8 q^{8} + 48 q^{10} + 14 q^{11} - 22 q^{14} - 52 q^{16} - 48 q^{17} - 78 q^{19} + 80 q^{22} + 68 q^{23} - 6 q^{25} + 126 q^{26} + 172 q^{28} - 64 q^{29} - 66 q^{31} - 12 q^{32} - 114 q^{35} - 46 q^{37} - 174 q^{38} - 348 q^{40} - 28 q^{43} + 108 q^{44} + 104 q^{46} + 222 q^{47} + 186 q^{49} + 68 q^{50} + 492 q^{52} + 32 q^{53} - 32 q^{56} - 148 q^{58} - 84 q^{59} + 180 q^{61} - 152 q^{64} + 78 q^{65} - 126 q^{67} - 36 q^{68} - 588 q^{70} - 244 q^{71} - 150 q^{73} - 38 q^{74} - 52 q^{77} - 54 q^{79} - 48 q^{80} + 324 q^{82} + 528 q^{85} - 158 q^{86} - 332 q^{88} + 60 q^{89} + 258 q^{91} + 168 q^{92} - 204 q^{94} + 150 q^{95} + 176 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.3.m.a 63.m 7.d $2$ $1.717$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(6\) \(-7\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\zeta_{6}q^{2}+(4-2\zeta_{6})q^{5}-7\zeta_{6}q^{7}+\cdots\)
63.3.m.b 63.m 7.d $2$ $1.717$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(13\) $\mathrm{U}(1)[D_{6}]$ \(q+(4-4\zeta_{6})q^{4}+(8-3\zeta_{6})q^{7}+(-7+\cdots)q^{13}+\cdots\)
63.3.m.c 63.m 7.d $2$ $1.717$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(9\) \(-7\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{4}+(6-3\zeta_{6})q^{5}+\cdots\)
63.3.m.d 63.m 7.d $2$ $1.717$ \(\Q(\sqrt{-3}) \) None \(3\) \(0\) \(-9\) \(13\) $\mathrm{SU}(2)[C_{6}]$ \(q+3\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{4}+(-6+3\zeta_{6})q^{5}+\cdots\)
63.3.m.e 63.m 7.d $4$ $1.717$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(0\) \(0\) \(0\) \(-26\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(-9+9\beta _{1})q^{4}+(\beta _{2}+2\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)