Properties

Label 102.2.h
Level $102$
Weight $2$
Character orbit 102.h
Rep. character $\chi_{102}(19,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $16$
Newform subspaces $2$
Sturm bound $36$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 102 = 2 \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 102.h (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 88 16 72
Cusp forms 56 16 40
Eisenstein series 32 0 32

Trace form

\( 16 q + 16 q^{5} + O(q^{10}) \) \( 16 q + 16 q^{5} - 16 q^{11} - 16 q^{14} - 16 q^{16} - 16 q^{19} - 16 q^{22} - 16 q^{23} - 16 q^{25} + 16 q^{26} + 16 q^{28} + 16 q^{34} - 32 q^{35} + 16 q^{37} - 16 q^{39} + 16 q^{41} + 16 q^{42} + 16 q^{44} + 32 q^{50} + 48 q^{53} + 32 q^{57} + 16 q^{59} - 16 q^{61} + 64 q^{65} + 16 q^{66} + 32 q^{67} + 16 q^{69} + 16 q^{70} - 48 q^{71} + 16 q^{73} - 16 q^{74} - 32 q^{75} + 16 q^{76} - 64 q^{77} - 32 q^{78} + 16 q^{79} - 16 q^{80} - 16 q^{83} - 16 q^{84} - 48 q^{85} - 32 q^{86} - 48 q^{87} - 16 q^{88} + 48 q^{91} - 16 q^{93} - 16 q^{94} + 16 q^{95} - 16 q^{99} + O(q^{100}) \)

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.h.a 102.h 17.d $8$ $0.814$ \(\Q(\zeta_{16})\) None 102.2.h.a \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots\)
102.2.h.b 102.h 17.d $8$ $0.814$ \(\Q(\zeta_{16})\) None 102.2.h.b \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\zeta_{16}^{6}q^{2}+\zeta_{16}q^{3}-\zeta_{16}^{4}q^{4}+(1+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(102, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)