Properties

Label 98.2.a
Level $98$
Weight $2$
Character orbit 98.a
Rep. character $\chi_{98}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $28$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 98.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(28\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(98))\).

Total New Old
Modular forms 22 3 19
Cusp forms 7 3 4
Eisenstein series 15 0 15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(7\)FrickeDim.
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(0\)
Minus space\(-\)\(3\)

Trace form

\( 3 q + q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{6} + q^{8} - q^{9} + O(q^{10}) \) \( 3 q + q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{6} + q^{8} - q^{9} - 4 q^{11} + 2 q^{12} + 4 q^{13} - 8 q^{15} + 3 q^{16} - 6 q^{17} - 3 q^{18} - 2 q^{19} - 4 q^{22} - 8 q^{23} - 2 q^{24} + q^{25} - 4 q^{26} - 4 q^{27} - 2 q^{29} - 8 q^{30} + 4 q^{31} + q^{32} + 6 q^{34} - q^{36} + 22 q^{37} + 2 q^{38} + 8 q^{39} - 6 q^{41} + 12 q^{43} - 4 q^{44} - 8 q^{46} + 12 q^{47} + 2 q^{48} + 11 q^{50} - 8 q^{51} + 4 q^{52} + 2 q^{53} + 4 q^{54} + 16 q^{57} + 10 q^{58} + 6 q^{59} - 8 q^{60} - 8 q^{61} - 4 q^{62} + 3 q^{64} + 20 q^{67} - 6 q^{68} - 24 q^{71} - 3 q^{72} - 2 q^{73} + 18 q^{74} - 10 q^{75} - 2 q^{76} - 8 q^{78} - 21 q^{81} + 6 q^{82} + 6 q^{83} - 8 q^{85} - 4 q^{86} - 12 q^{87} - 4 q^{88} + 6 q^{89} - 8 q^{92} - 16 q^{93} - 12 q^{94} - 40 q^{95} - 2 q^{96} + 10 q^{97} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(98))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7
98.2.a.a 98.a 1.a $1$ $0.783$ \(\Q\) None \(-1\) \(2\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots\)
98.2.a.b 98.a 1.a $2$ $0.783$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-2\beta q^{5}+\beta q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(98))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(98)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)