Properties

Label 100.2.a
Level 100
Weight 2
Character orbit a
Rep. character \(\chi_{100}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 30
Trace bound 0

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Defining parameters

Level: \( N \) = \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 100.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(100))\).

Total New Old
Modular forms 24 1 23
Cusp forms 7 1 6
Eisenstein series 17 0 17

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

\(2\)\(5\)FrickeDim.
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\(q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 10q^{43} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 3q^{49} \) \(\mathstrut +\mathstrut 12q^{51} \) \(\mathstrut +\mathstrut 6q^{53} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 2q^{63} \) \(\mathstrut -\mathstrut 2q^{67} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut -\mathstrut 12q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 11q^{81} \) \(\mathstrut -\mathstrut 6q^{83} \) \(\mathstrut +\mathstrut 12q^{87} \) \(\mathstrut -\mathstrut 6q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 8q^{93} \) \(\mathstrut -\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(100))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
100.2.a.a \(1\) \(0.799\) \(\Q\) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(+\) \(q+2q^{3}-2q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(100)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)