Properties

Label 147.8.e
Level $147$
Weight $8$
Character orbit 147.e
Rep. character $\chi_{147}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $94$
Newform subspaces $16$
Sturm bound $149$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 16 \)
Sturm bound: \(149\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(147, [\chi])\).

Total New Old
Modular forms 278 94 184
Cusp forms 246 94 152
Eisenstein series 32 0 32

Trace form

\( 94 q + 28 q^{2} - 27 q^{3} - 3436 q^{4} - 2 q^{5} + 864 q^{6} - 6876 q^{8} - 34263 q^{9} - 10266 q^{10} + 3242 q^{11} - 3456 q^{12} + 10134 q^{13} - 21276 q^{15} - 293764 q^{16} - 46200 q^{17} + 20412 q^{18}+ \cdots - 4726836 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
147.8.e.a 147.e 7.c $2$ $45.921$ \(\Q(\sqrt{-3}) \) None 3.8.a.a \(-6\) \(-27\) \(390\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-6\zeta_{6}q^{2}+(-3^{3}+3^{3}\zeta_{6})q^{3}+(92+\cdots)q^{4}+\cdots\)
147.8.e.b 147.e 7.c $2$ $45.921$ \(\Q(\sqrt{-3}) \) None 3.8.a.a \(-6\) \(27\) \(-390\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-6\zeta_{6}q^{2}+(3^{3}-3^{3}\zeta_{6})q^{3}+(92-92\zeta_{6})q^{4}+\cdots\)
147.8.e.c 147.e 7.c $2$ $45.921$ \(\Q(\sqrt{-3}) \) None 21.8.a.a \(-2\) \(-27\) \(278\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-3^{3}+3^{3}\zeta_{6})q^{3}+(124+\cdots)q^{4}+\cdots\)
147.8.e.d 147.e 7.c $2$ $45.921$ \(\Q(\sqrt{-3}) \) None 21.8.a.a \(-2\) \(27\) \(-278\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(3^{3}-3^{3}\zeta_{6})q^{3}+(124-124\zeta_{6})q^{4}+\cdots\)
147.8.e.e 147.e 7.c $4$ $45.921$ \(\Q(\sqrt{-3}, \sqrt{67})\) None 21.8.a.c \(-12\) \(-54\) \(-24\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-6+\beta _{1}-6\beta _{2})q^{2}+3^{3}\beta _{2}q^{3}+\cdots\)
147.8.e.f 147.e 7.c $4$ $45.921$ \(\Q(\sqrt{-3}, \sqrt{67})\) None 21.8.a.c \(-12\) \(54\) \(24\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-6+\beta _{1}-6\beta _{2})q^{2}-3^{3}\beta _{2}q^{3}+\cdots\)
147.8.e.g 147.e 7.c $4$ $45.921$ \(\Q(\sqrt{-3}, \sqrt{-355})\) None 21.8.a.b \(9\) \(-54\) \(-360\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4+4\beta _{1}-\beta _{3})q^{2}+3^{3}\beta _{1}q^{3}+(154\beta _{1}+\cdots)q^{4}+\cdots\)
147.8.e.h 147.e 7.c $4$ $45.921$ \(\Q(\sqrt{-3}, \sqrt{-355})\) None 21.8.a.b \(9\) \(54\) \(360\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4+4\beta _{1}-\beta _{3})q^{2}-3^{3}\beta _{1}q^{3}+(154\beta _{1}+\cdots)q^{4}+\cdots\)
147.8.e.i 147.e 7.c $6$ $45.921$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 21.8.a.d \(3\) \(-81\) \(114\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}-\beta _{3})q^{2}-3^{3}\beta _{1}q^{3}+(-75\beta _{1}+\cdots)q^{4}+\cdots\)
147.8.e.j 147.e 7.c $6$ $45.921$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 21.8.a.d \(3\) \(81\) \(-114\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}-\beta _{3})q^{2}+3^{3}\beta _{1}q^{3}+(-75\beta _{1}+\cdots)q^{4}+\cdots\)
147.8.e.k 147.e 7.c $8$ $45.921$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 21.8.e.a \(1\) \(108\) \(196\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{6}q^{2}-3^{3}\beta _{4}q^{3}+(-2\beta _{1}+5^{2}\beta _{4}+\cdots)q^{4}+\cdots\)
147.8.e.l 147.e 7.c $8$ $45.921$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 147.8.a.f \(15\) \(-108\) \(-504\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\beta _{1}+\beta _{3})q^{2}-3^{3}\beta _{1}q^{3}+(-110\beta _{1}+\cdots)q^{4}+\cdots\)
147.8.e.m 147.e 7.c $8$ $45.921$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 147.8.a.f \(15\) \(108\) \(504\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\beta _{1}+\beta _{3})q^{2}+3^{3}\beta _{1}q^{3}+(-110\beta _{1}+\cdots)q^{4}+\cdots\)
147.8.e.n 147.e 7.c $10$ $45.921$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 21.8.e.b \(-15\) \(-135\) \(-198\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3-\beta _{1}-3\beta _{4})q^{2}+3^{3}\beta _{4}q^{3}+\cdots\)
147.8.e.o 147.e 7.c $12$ $45.921$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 147.8.a.l \(14\) \(-162\) \(500\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{1}-\beta _{5})q^{2}+3^{3}\beta _{1}q^{3}+(72\beta _{1}+\cdots)q^{4}+\cdots\)
147.8.e.p 147.e 7.c $12$ $45.921$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 147.8.a.l \(14\) \(162\) \(-500\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{1}-\beta _{5})q^{2}-3^{3}\beta _{1}q^{3}+(72\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(147, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)