Properties

Label 102.2.b
Level $102$
Weight $2$
Character orbit 102.b
Rep. character $\chi_{102}(67,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 102 = 2 \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 102.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(102, [\chi])\).

Total New Old
Modular forms 22 2 20
Cusp forms 14 2 12
Eisenstein series 8 0 8

Trace form

\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 2 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 2 q^{9} - 12 q^{13} + 4 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{21} + 2 q^{25} - 12 q^{26} + 4 q^{30} + 2 q^{32} - 2 q^{34} + 8 q^{35} - 2 q^{36} - 4 q^{42} + 8 q^{43} + 16 q^{47} + 6 q^{49} + 2 q^{50} + 8 q^{51} - 12 q^{52} - 12 q^{53} + 4 q^{60} + 2 q^{64} + 16 q^{67} - 2 q^{68} + 12 q^{69} + 8 q^{70} - 2 q^{72} + 2 q^{81} - 32 q^{83} - 4 q^{84} - 16 q^{85} + 8 q^{86} - 12 q^{87} + 20 q^{89} - 20 q^{93} + 16 q^{94} + 6 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(102, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
102.2.b.a 102.b 17.b $2$ $0.814$ \(\Q(\sqrt{-1}) \) None 102.2.b.a \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}+q^{4}-2iq^{5}+iq^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(102, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(102, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)