Properties

Label 104.2.o
Level $104$
Weight $2$
Character orbit 104.o
Rep. character $\chi_{104}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
Sturm bound $28$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 104 = 2^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 104.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
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 36 8 28
Cusp forms 20 8 12
Eisenstein series 16 0 16

Trace form

\( 8 q + 2 q^{3} - 6 q^{7} - 6 q^{9} + O(q^{10}) \) \( 8 q + 2 q^{3} - 6 q^{7} - 6 q^{9} + 6 q^{11} + 6 q^{13} - 6 q^{19} + 2 q^{23} - 20 q^{25} - 28 q^{27} - 8 q^{29} + 6 q^{33} + 16 q^{35} - 24 q^{37} - 14 q^{39} + 12 q^{41} + 6 q^{43} + 30 q^{45} + 2 q^{49} + 68 q^{51} + 20 q^{53} + 16 q^{55} + 18 q^{59} - 4 q^{61} + 36 q^{63} + 14 q^{65} - 42 q^{67} - 18 q^{69} - 54 q^{71} - 22 q^{75} - 60 q^{77} + 16 q^{79} - 20 q^{81} + 6 q^{85} - 10 q^{87} - 18 q^{89} - 46 q^{91} + 36 q^{93} + 16 q^{95} + 30 q^{97} + O(q^{100}) \)

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.o.a 104.o 13.e $8$ $0.830$ 8.0.195105024.2 None \(0\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+(\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(104, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)