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Properties

Label 98.5.d
Level $98$
Weight $5$
Character orbit 98.d
Rep. character $\chi_{98}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $4$
Sturm bound $70$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 98.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(70\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(98, [\chi])\).

Total New Old
Modular forms 128 28 100
Cusp forms 96 28 68
Eisenstein series 32 0 32

Trace form

\( 28 q + 18 q^{3} - 112 q^{4} - 54 q^{5} + 280 q^{9} + O(q^{10}) \) \( 28 q + 18 q^{3} - 112 q^{4} - 54 q^{5} + 280 q^{9} + 96 q^{10} + 210 q^{11} - 144 q^{12} + 924 q^{15} - 896 q^{16} - 918 q^{17} - 896 q^{18} - 30 q^{19} + 448 q^{22} + 546 q^{23} + 768 q^{24} + 2520 q^{25} + 1728 q^{26} - 6216 q^{29} - 448 q^{30} + 546 q^{31} - 1062 q^{33} - 4480 q^{36} + 2170 q^{37} + 4320 q^{38} - 2464 q^{39} - 768 q^{40} + 16408 q^{43} + 1680 q^{44} - 5724 q^{45} - 5376 q^{46} - 702 q^{47} - 4242 q^{51} + 384 q^{52} + 7434 q^{53} + 1440 q^{54} - 1652 q^{57} - 11648 q^{58} - 12366 q^{59} - 3696 q^{60} - 7686 q^{61} + 14336 q^{64} + 18480 q^{65} + 3456 q^{66} + 13426 q^{67} + 7344 q^{68} - 16968 q^{71} - 7168 q^{72} + 17274 q^{73} - 7392 q^{74} + 5220 q^{75} - 17920 q^{78} + 8274 q^{79} + 3456 q^{80} - 16254 q^{81} - 9984 q^{82} - 10836 q^{85} + 13440 q^{86} + 12276 q^{87} - 1792 q^{88} + 12474 q^{89} - 8736 q^{92} - 40698 q^{93} - 15168 q^{94} - 2562 q^{95} - 6144 q^{96} - 4648 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(98, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
98.5.d.a 98.d 7.d $4$ $10.130$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(18\) \(-54\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(6-2\beta _{1}+3\beta _{2}+2\beta _{3})q^{3}+\cdots\)
98.5.d.b 98.d 7.d $8$ $10.130$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\beta _{6}q^{2}+3\beta _{3}q^{3}+(-8-8\beta _{4})q^{4}+\cdots\)
98.5.d.c 98.d 7.d $8$ $10.130$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\beta _{6}q^{2}+(4\beta _{1}+7\beta _{3})q^{3}+(-8-8\beta _{4}+\cdots)q^{4}+\cdots\)
98.5.d.d 98.d 7.d $8$ $10.130$ 8.0.\(\cdots\).28 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{5}-\beta _{6})q^{2}+(\beta _{3}-\beta _{4})q^{3}+(-8+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(98, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)