Properties

Label 102.2.a
Level 102
Weight 2
Character orbit a
Rep. character \(\chi_{102}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 3
Sturm bound 36
Trace bound 3

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Defining parameters

Level: \( N \) = \( 102 = 2 \cdot 3 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 102.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(36\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(102))\).

Total New Old
Modular forms 22 3 19
Cusp forms 15 3 12
Eisenstein series 7 0 7

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

\(2\)\(3\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\(3q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 3q^{16} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 3q^{34} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 3q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 10q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 6q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 3q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut -\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 28q^{67} \) \(\mathstrut -\mathstrut q^{68} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut q^{72} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 17q^{75} \) \(\mathstrut +\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut 3q^{81} \) \(\mathstrut +\mathstrut 14q^{82} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 4q^{84} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 20q^{86} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 26q^{89} \) \(\mathstrut +\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 6q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(102))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 17
102.2.a.a \(1\) \(0.814\) \(\Q\) None \(-1\) \(-1\) \(-4\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-2q^{7}+\cdots\)
102.2.a.b \(1\) \(0.814\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
102.2.a.c \(1\) \(0.814\) \(\Q\) None \(1\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(102))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(102)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)