Properties

Label 104.2.f
Level $104$
Weight $2$
Character orbit 104.f
Rep. character $\chi_{104}(25,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $28$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 104 = 2^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 104.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(104, [\chi])\).

Total New Old
Modular forms 18 4 14
Cusp forms 10 4 6
Eisenstein series 8 0 8

Trace form

\( 4 q - 2 q^{3} + 6 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{3} + 6 q^{9} - 6 q^{13} - 6 q^{17} + 4 q^{23} + 2 q^{25} - 14 q^{27} - 4 q^{29} - 22 q^{35} + 20 q^{39} + 30 q^{43} - 14 q^{49} - 14 q^{51} + 16 q^{53} + 32 q^{55} + 28 q^{61} - 14 q^{65} - 36 q^{69} + 16 q^{75} + 24 q^{77} - 28 q^{79} - 28 q^{81} - 32 q^{87} - 2 q^{91} - 4 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(104, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
104.2.f.a 104.f 13.b $4$ $0.830$ \(\Q(i, \sqrt{17})\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{3})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(104, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(104, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 3}\)