Properties

Label 98.2.c
Level $98$
Weight $2$
Character orbit 98.c
Rep. character $\chi_{98}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $3$
Sturm bound $28$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(28\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(98, [\chi])\).

Total New Old
Modular forms 44 8 36
Cusp forms 12 8 4
Eisenstein series 32 0 32

Trace form

\( 8 q - 4 q^{4} + O(q^{10}) \) \( 8 q - 4 q^{4} + 4 q^{11} - 16 q^{15} - 4 q^{16} + 4 q^{18} - 8 q^{22} + 8 q^{23} + 4 q^{25} - 16 q^{29} + 8 q^{30} - 24 q^{37} - 16 q^{39} + 40 q^{43} + 4 q^{44} + 8 q^{46} + 32 q^{50} + 20 q^{51} - 8 q^{53} + 24 q^{57} - 16 q^{58} + 8 q^{60} + 8 q^{64} - 16 q^{67} - 48 q^{71} + 4 q^{72} - 16 q^{74} - 32 q^{78} - 8 q^{79} + 32 q^{81} - 16 q^{85} + 12 q^{86} + 4 q^{88} - 16 q^{92} + 8 q^{93} + 40 q^{95} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(98, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
98.2.c.a 98.c 7.c $2$ $0.783$ \(\Q(\sqrt{-3}) \) None 14.2.a.a \(1\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
98.2.c.b 98.c 7.c $2$ $0.783$ \(\Q(\sqrt{-3}) \) None 14.2.a.a \(1\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
98.2.c.c 98.c 7.c $4$ $0.783$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 98.2.a.b \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

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