Properties

Label 126.2.a
Level 126
Weight 2
Character orbit a
Rep. character \(\chi_{126}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 48
Trace bound 2

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Defining parameters

Level: \( N \) = \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 126.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(126))\).

Total New Old
Modular forms 32 2 30
Cusp forms 17 2 15
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.

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

Trace form

\(2q \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 6q^{25} \) \(\mathstrut -\mathstrut 10q^{26} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 4q^{34} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 6q^{38} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut +\mathstrut 2q^{52} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 2q^{56} \) \(\mathstrut +\mathstrut 4q^{58} \) \(\mathstrut +\mathstrut 2q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut -\mathstrut 4q^{62} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut -\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 12q^{89} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut +\mathstrut 12q^{94} \) \(\mathstrut -\mathstrut 8q^{95} \) \(\mathstrut -\mathstrut 24q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(126))\) 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 7
126.2.a.a \(1\) \(1.006\) \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
126.2.a.b \(1\) \(1.006\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{13}+q^{14}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(126))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(126)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 2}\)