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Properties

Label 98.3.d
Level $98$
Weight $3$
Character orbit 98.d
Rep. character $\chi_{98}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $2$
Sturm bound $42$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 98.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(42\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(98, [\chi])\).

Total New Old
Modular forms 72 12 60
Cusp forms 40 12 28
Eisenstein series 32 0 32

Trace form

\( 12 q + 6 q^{3} - 12 q^{4} + 6 q^{5} + 28 q^{9} + O(q^{10}) \) \( 12 q + 6 q^{3} - 12 q^{4} + 6 q^{5} + 28 q^{9} - 24 q^{10} - 30 q^{11} - 12 q^{12} + 60 q^{15} - 24 q^{16} + 30 q^{17} + 40 q^{18} - 6 q^{19} - 40 q^{22} - 50 q^{23} - 24 q^{24} + 40 q^{25} - 24 q^{26} - 80 q^{29} + 20 q^{30} + 42 q^{31} + 90 q^{33} - 112 q^{36} + 66 q^{37} + 12 q^{38} + 92 q^{39} + 48 q^{40} - 360 q^{43} - 60 q^{44} - 144 q^{45} - 60 q^{46} - 174 q^{47} + 272 q^{50} - 90 q^{51} + 72 q^{52} + 18 q^{53} + 36 q^{54} + 652 q^{57} + 128 q^{58} + 78 q^{59} - 60 q^{60} + 42 q^{61} + 96 q^{64} - 84 q^{65} + 144 q^{66} - 314 q^{67} - 60 q^{68} + 40 q^{71} + 80 q^{72} - 318 q^{73} + 120 q^{74} - 132 q^{75} - 160 q^{78} + 302 q^{79} - 24 q^{80} - 114 q^{81} + 120 q^{82} - 612 q^{85} - 40 q^{86} + 144 q^{87} + 40 q^{88} + 378 q^{89} + 200 q^{92} - 330 q^{93} + 12 q^{94} + 50 q^{95} + 48 q^{96} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(98, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
98.3.d.a 98.d 7.d $4$ $2.670$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(6\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
98.3.d.b 98.d 7.d $8$ $2.670$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{2}+(2\beta _{1}+2\beta _{3})q^{3}+(-2-2\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(98, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)