Properties

Label 102.2.i
Level $102$
Weight $2$
Character orbit 102.i
Rep. character $\chi_{102}(5,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $48$
Newform subspaces $2$
Sturm bound $36$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 102 = 2 \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 102.i (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 51 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 176 48 128
Cusp forms 112 48 64
Eisenstein series 64 0 64

Trace form

\( 48 q + O(q^{10}) \) \( 48 q - 8 q^{12} - 48 q^{15} - 32 q^{18} - 48 q^{21} - 8 q^{24} - 32 q^{25} - 32 q^{31} - 32 q^{37} + 32 q^{39} + 48 q^{42} - 16 q^{43} + 64 q^{45} + 32 q^{46} + 64 q^{49} + 64 q^{51} + 32 q^{52} + 56 q^{54} + 64 q^{55} + 72 q^{57} + 32 q^{58} + 32 q^{60} + 32 q^{61} + 8 q^{66} - 32 q^{69} - 32 q^{70} - 128 q^{73} - 48 q^{75} - 64 q^{79} - 8 q^{81} - 128 q^{82} - 64 q^{85} + 48 q^{87} - 32 q^{88} - 128 q^{91} + 64 q^{93} - 64 q^{94} - 32 q^{97} + 40 q^{99} + O(q^{100}) \)

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.i.a 102.i 51.i $24$ $0.814$ None 102.2.i.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
102.2.i.b 102.i 51.i $24$ $0.814$ None 102.2.i.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

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

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