Properties

Label 196.8.e
Level $196$
Weight $8$
Character orbit 196.e
Rep. character $\chi_{196}(165,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $46$
Newform subspaces $7$
Sturm bound $224$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 196.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 7 \)
Sturm bound: \(224\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(196, [\chi])\).

Total New Old
Modular forms 416 46 370
Cusp forms 368 46 322
Eisenstein series 48 0 48

Trace form

\( 46 q - 27 q^{3} - 249 q^{5} - 14136 q^{9} - 9353 q^{11} + 26988 q^{13} - 29906 q^{15} - 3609 q^{17} + 12403 q^{19} + 31025 q^{23} - 226710 q^{25} - 161550 q^{27} - 61372 q^{29} + 20181 q^{31} - 264239 q^{33}+ \cdots + 99876892 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(196, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
196.8.e.a 196.e 7.c $4$ $61.227$ \(\Q(\sqrt{-3}, \sqrt{3529})\) None 28.8.a.a \(0\) \(-14\) \(42\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-7\beta _{1}-\beta _{2})q^{3}+(21-21\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)
196.8.e.b 196.e 7.c $4$ $61.227$ \(\Q(\sqrt{-3}, \sqrt{1009})\) None 28.8.a.b \(0\) \(-14\) \(294\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-7\beta _{1}-\beta _{2})q^{3}+(147-147\beta _{1}+\cdots)q^{5}+\cdots\)
196.8.e.c 196.e 7.c $4$ $61.227$ \(\Q(\sqrt{-3}, \sqrt{1009})\) None 28.8.a.b \(0\) \(14\) \(-294\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(7\beta _{1}+\beta _{2})q^{3}+(-147+147\beta _{1}+\cdots)q^{5}+\cdots\)
196.8.e.d 196.e 7.c $4$ $61.227$ \(\Q(\sqrt{-3}, \sqrt{3529})\) None 28.8.a.a \(0\) \(14\) \(-42\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(7\beta _{1}+\beta _{2})q^{3}+(-21+21\beta _{1}-3\beta _{2}+\cdots)q^{5}+\cdots\)
196.8.e.e 196.e 7.c $8$ $61.227$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 196.8.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{2}+\beta _{4})q^{3}+\beta _{7}q^{5}+(-1769\beta _{1}+\cdots)q^{9}+\cdots\)
196.8.e.f 196.e 7.c $10$ $61.227$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 28.8.e.a \(0\) \(-27\) \(-249\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-5-5\beta _{1}-\beta _{2}+\beta _{4})q^{3}+(7^{2}\beta _{1}+\cdots)q^{5}+\cdots\)
196.8.e.g 196.e 7.c $12$ $61.227$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 196.8.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{2}-\beta _{3})q^{3}+(-\beta _{3}-\beta _{8}+\beta _{9}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(196, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(196, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)