Properties

Label 98.2.a
Level 98
Weight 2
Character orbit a
Rep. character \(\chi_{98}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(98))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
98.2.a.a \(1\) \(0.783\) \(\Q\) None \(-1\) \(2\) \(0\) \(0\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots\)
98.2.a.b \(2\) \(0.783\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+q^{2}+\beta q^{3}+q^{4}-2\beta q^{5}+\beta q^{6}+\cdots\)

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

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