Properties

Label 106.2.a
Level 106
Weight 2
Character orbit a
Rep. character \(\chi_{106}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 4
Sturm bound 27
Trace bound 3

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Defining parameters

Level: \( N \) = \( 106 = 2 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 106.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(27\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(106))\).

Total New Old
Modular forms 15 4 11
Cusp forms 12 4 8
Eisenstein series 3 0 3

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

\(2\)\(53\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(3\)

Trace form

\(4q \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut +\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 20q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut +\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 14q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut +\mathstrut 12q^{45} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 2q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 6q^{57} \) \(\mathstrut +\mathstrut 16q^{58} \) \(\mathstrut +\mathstrut 22q^{59} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 2q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 14q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 36q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 32q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 16q^{77} \) \(\mathstrut +\mathstrut 22q^{78} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 20q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 8q^{85} \) \(\mathstrut -\mathstrut 8q^{86} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 16q^{98} \) \(\mathstrut +\mathstrut 10q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(106))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 53
106.2.a.a \(1\) \(0.846\) \(\Q\) None \(-1\) \(-1\) \(-4\) \(0\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{8}+\cdots\)
106.2.a.b \(1\) \(0.846\) \(\Q\) None \(-1\) \(2\) \(1\) \(-2\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-2q^{7}+\cdots\)
106.2.a.c \(1\) \(0.846\) \(\Q\) None \(1\) \(-2\) \(3\) \(2\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}+2q^{7}+\cdots\)
106.2.a.d \(1\) \(0.846\) \(\Q\) None \(1\) \(1\) \(0\) \(-4\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(106))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(106)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 2}\)