Properties

Label 104.2.a
Level $104$
Weight $2$
Character orbit 104.a
Rep. character $\chi_{104}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(104))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 13
104.2.a.a 104.a 1.a $1$ $0.830$ \(\Q\) None \(0\) \(1\) \(-1\) \(5\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+5q^{7}-2q^{9}-2q^{11}+\cdots\)
104.2.a.b 104.a 1.a $2$ $0.830$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(3\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2-\beta )q^{5}-\beta q^{7}+(1+\beta )q^{9}+\cdots\)

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

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