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

Related objects

Downloads

Learn more about

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

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

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

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