Properties

Label 104.2.e
Level $104$
Weight $2$
Character orbit 104.e
Rep. character $\chi_{104}(77,\cdot)$
Character field $\Q$
Dimension $12$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(28\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 16 16 0
Cusp forms 12 12 0
Eisenstein series 4 4 0

Trace form

\( 12 q - 2 q^{4} - 12 q^{9} + O(q^{10}) \) \( 12 q - 2 q^{4} - 12 q^{9} - 10 q^{10} + 14 q^{12} - 6 q^{14} - 6 q^{16} - 8 q^{17} + 12 q^{22} + 8 q^{23} - 4 q^{25} - 2 q^{26} + 18 q^{30} - 36 q^{36} - 36 q^{38} + 16 q^{39} - 18 q^{40} + 34 q^{42} + 30 q^{48} + 12 q^{49} + 12 q^{52} - 56 q^{55} + 38 q^{56} + 40 q^{62} - 38 q^{64} + 16 q^{66} + 46 q^{68} - 34 q^{74} - 34 q^{78} + 16 q^{79} + 4 q^{81} - 40 q^{82} + 8 q^{87} + 48 q^{88} + 48 q^{90} - 8 q^{92} - 46 q^{94} - 16 q^{95} + O(q^{100}) \)

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.e.a 104.e 104.e $2$ $0.830$ \(\Q(\sqrt{-1}) \) None 104.2.e.a \(-2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(i-1)q^{2}-i q^{3}-2 i q^{4}+q^{5}+\cdots\)
104.2.e.b 104.e 104.e $2$ $0.830$ \(\Q(\sqrt{-1}) \) None 104.2.e.a \(2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(i+1)q^{2}+i q^{3}+2 i q^{4}-q^{5}+\cdots\)
104.2.e.c 104.e 104.e $8$ $0.830$ 8.0.4521217600.1 None 104.2.e.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{3}-\beta _{5}q^{4}-\beta _{6}q^{5}+\cdots\)