Properties

Label 104.2.a
Level 104
Weight 2
Character orbit a
Rep. character \(\chi_{104}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 28
Trace bound 1

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Defining parameters

Level: \( N \) = \( 104 = 2^{3} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 104.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 \(M_{2}(\Gamma_0(104))\).

Total New Old
Modular forms 18 3 15
Cusp forms 11 3 8
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.

\(2\)\(13\)FrickeDim.
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(3\)

Trace form

\(3q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 10q^{29} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 20q^{33} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 14q^{43} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut +\mathstrut 22q^{51} \) \(\mathstrut -\mathstrut 14q^{53} \) \(\mathstrut +\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 28q^{75} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut +\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 28q^{83} \) \(\mathstrut -\mathstrut 24q^{85} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{97} \) \(\mathstrut -\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(104))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 13
104.2.a.a \(1\) \(0.830\) \(\Q\) None \(0\) \(1\) \(-1\) \(5\) \(-\) \(+\) \(q+q^{3}-q^{5}+5q^{7}-2q^{9}-2q^{11}+\cdots\)
104.2.a.b \(2\) \(0.830\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(3\) \(-1\) \(+\) \(-\) \(q+\beta q^{3}+(2-\beta )q^{5}-\beta q^{7}+(1+\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(104))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(104)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 2}\)