Properties

Label 104.2.s
Level $104$
Weight $2$
Character orbit 104.s
Rep. character $\chi_{104}(69,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $3$
Sturm bound $28$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 104 = 2^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 104.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(28\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 32 32 0
Cusp forms 24 24 0
Eisenstein series 8 8 0

Trace form

\( 24 q - 3 q^{2} - q^{4} + 6 q^{6} - 6 q^{7} + 6 q^{9} + O(q^{10}) \) \( 24 q - 3 q^{2} - q^{4} + 6 q^{6} - 6 q^{7} + 6 q^{9} + q^{10} - 8 q^{12} - 24 q^{15} - 9 q^{16} - 4 q^{17} - 27 q^{20} + 18 q^{22} - 14 q^{23} - 36 q^{24} + 4 q^{25} + 29 q^{26} - 12 q^{30} - 3 q^{32} - 6 q^{33} + 9 q^{36} + 14 q^{39} - 6 q^{40} - 12 q^{41} + 14 q^{42} + 42 q^{46} + 30 q^{48} + 6 q^{49} + 18 q^{50} + 36 q^{52} - 18 q^{54} + 20 q^{55} - 8 q^{56} - 15 q^{58} - 4 q^{62} - 24 q^{63} + 50 q^{64} - 30 q^{65} + 8 q^{66} + 29 q^{68} - 6 q^{71} + 87 q^{72} - 35 q^{74} + 36 q^{76} - 68 q^{78} + 32 q^{79} + 15 q^{80} + 8 q^{81} + 19 q^{82} - 48 q^{84} + 22 q^{87} - 24 q^{88} - 6 q^{89} - 114 q^{90} + 68 q^{92} - 20 q^{94} + 40 q^{95} - 30 q^{97} - 123 q^{98} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
104.2.s.a 104.s 104.s $4$ $0.830$ \(\Q(\zeta_{12})\) None 104.2.s.a \(-4\) \(-6\) \(-8\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
104.2.s.b 104.s 104.s $4$ $0.830$ \(\Q(\zeta_{12})\) None 104.2.s.a \(-2\) \(6\) \(8\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots\)
104.2.s.c 104.s 104.s $16$ $0.830$ 16.0.\(\cdots\).2 None 104.2.s.c \(3\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{14})q^{2}+(\beta _{3}-\beta _{11})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)