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Properties

Label 102.2.h
Level 102
Weight 2
Character orbit h
Rep. character \(\chi_{102}(19,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 16
Newforms 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: \(\Q(\zeta_{8})\)
Newforms: \( 2 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(102, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
102.2.h.a \(8\) \(0.814\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(8\) \(0\) \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots\)
102.2.h.b \(8\) \(0.814\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(8\) \(0\) \(q+\zeta_{16}^{6}q^{2}+\zeta_{16}q^{3}-\zeta_{16}^{4}q^{4}+(1+\cdots)q^{5}+\cdots\)

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

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