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Properties

Label 98.6.c
Level $98$
Weight $6$
Character orbit 98.c
Rep. character $\chi_{98}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $9$
Sturm bound $84$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 9 \)
Sturm bound: \(84\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(98, [\chi])\).

Total New Old
Modular forms 156 32 124
Cusp forms 124 32 92
Eisenstein series 32 0 32

Trace form

\( 32 q - 256 q^{4} + 28 q^{5} - 224 q^{6} - 504 q^{9} + 448 q^{10} - 612 q^{11} - 3360 q^{13} + 5200 q^{15} - 4096 q^{16} + 2996 q^{17} - 2768 q^{18} - 616 q^{19} - 896 q^{20} - 4736 q^{22} - 880 q^{23} + 1792 q^{24}+ \cdots - 37544 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(98, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
98.6.c.a 98.c 7.c $2$ $15.718$ \(\Q(\sqrt{-3}) \) None 14.6.a.b \(-4\) \(-8\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\zeta_{6}q^{2}+(-8+8\zeta_{6})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
98.6.c.b 98.c 7.c $2$ $15.718$ \(\Q(\sqrt{-3}) \) None 14.6.a.b \(-4\) \(8\) \(10\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\zeta_{6}q^{2}+(8-8\zeta_{6})q^{3}+(-2^{4}+2^{4}\zeta_{6})q^{4}+\cdots\)
98.6.c.c 98.c 7.c $2$ $15.718$ \(\Q(\sqrt{-3}) \) None 14.6.a.a \(4\) \(-10\) \(-84\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\zeta_{6}q^{2}+(-10+10\zeta_{6})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
98.6.c.d 98.c 7.c $2$ $15.718$ \(\Q(\sqrt{-3}) \) None 14.6.a.a \(4\) \(10\) \(84\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\zeta_{6}q^{2}+(10-10\zeta_{6})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
98.6.c.e 98.c 7.c $4$ $15.718$ \(\Q(\sqrt{-3}, \sqrt{79})\) None 14.6.c.a \(-8\) \(14\) \(70\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\beta _{2}q^{2}+(7+\beta _{1}+7\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
98.6.c.f 98.c 7.c $4$ $15.718$ \(\Q(\sqrt{-3}, \sqrt{130})\) None 14.6.c.b \(8\) \(-14\) \(-42\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\beta _{2}q^{2}+(-7-\beta _{1}-7\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
98.6.c.g 98.c 7.c $4$ $15.718$ \(\Q(\sqrt{-3}, \sqrt{46})\) None 98.6.a.e \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\beta _{2}q^{2}+\beta _{1}q^{3}+(-2^{4}-2^{4}\beta _{2}+\cdots)q^{4}+\cdots\)
98.6.c.h 98.c 7.c $4$ $15.718$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 98.6.a.d \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\beta _{2}q^{2}+6\beta _{1}q^{3}+(-2^{4}-2^{4}\beta _{2}+\cdots)q^{4}+\cdots\)
98.6.c.i 98.c 7.c $8$ $15.718$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 98.6.a.i \(-16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\beta _{1}q^{2}+\beta _{5}q^{3}+(-2^{4}-2^{4}\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

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