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Properties

Label 243.2.c
Level $243$
Weight $2$
Character orbit 243.c
Rep. character $\chi_{243}(82,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $6$
Sturm bound $54$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 243 = 3^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 243.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(54\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(243, [\chi])\).

Total New Old
Modular forms 72 24 48
Cusp forms 36 24 12
Eisenstein series 36 0 36

Trace form

\( 24 q - 12 q^{4} + 3 q^{7} + O(q^{10}) \) \( 24 q - 12 q^{4} + 3 q^{7} + 3 q^{13} - 12 q^{16} - 6 q^{19} - 12 q^{25} - 24 q^{28} + 12 q^{31} + 18 q^{34} - 6 q^{37} + 18 q^{40} + 12 q^{43} - 36 q^{46} - 9 q^{49} + 12 q^{52} - 36 q^{55} + 18 q^{58} - 24 q^{61} - 12 q^{64} - 24 q^{67} + 18 q^{70} + 48 q^{73} + 30 q^{76} + 21 q^{79} + 144 q^{82} - 72 q^{85} + 36 q^{88} + 24 q^{91} + 36 q^{94} - 69 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(243, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
243.2.c.a 243.c 9.c $2$ $1.940$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 243.2.a.b \(0\) \(0\) \(0\) \(-5\) $\mathrm{U}(1)[D_{3}]$ \(q+2\zeta_{6}q^{4}+(-5+5\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
243.2.c.b 243.c 9.c $2$ $1.940$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 243.2.a.a \(0\) \(0\) \(0\) \(4\) $\mathrm{U}(1)[D_{3}]$ \(q+2\zeta_{6}q^{4}+(4-4\zeta_{6})q^{7}+7\zeta_{6}q^{13}+\cdots\)
243.2.c.c 243.c 9.c $4$ $1.940$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 243.2.a.d \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-4+4\beta _{1})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
243.2.c.d 243.c 9.c $4$ $1.940$ \(\Q(\zeta_{12})\) None 243.2.a.c \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
243.2.c.e 243.c 9.c $6$ $1.940$ \(\Q(\zeta_{18})\) None 243.2.a.e \(-3\) \(0\) \(-6\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}+\cdots)q^{4}+\cdots\)
243.2.c.f 243.c 9.c $6$ $1.940$ \(\Q(\zeta_{18})\) None 243.2.a.e \(3\) \(0\) \(6\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(243, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(243, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)