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Properties

Label 102.2.f
Level $102$
Weight $2$
Character orbit 102.f
Rep. character $\chi_{102}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
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.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
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 44 4 40
Cusp forms 28 4 24
Eisenstein series 16 0 16

Trace form

\( 4 q - 4 q^{4} - 4 q^{5} + 8 q^{7} + O(q^{10}) \) \( 4 q - 4 q^{4} - 4 q^{5} + 8 q^{7} - 4 q^{10} - 8 q^{14} + 4 q^{16} - 12 q^{17} + 4 q^{18} + 4 q^{20} + 8 q^{21} + 8 q^{23} - 8 q^{28} + 4 q^{29} + 8 q^{30} + 8 q^{31} - 16 q^{33} - 12 q^{37} + 16 q^{38} - 8 q^{39} + 4 q^{40} - 20 q^{41} + 4 q^{45} - 8 q^{46} + 16 q^{47} + 4 q^{50} + 8 q^{51} - 32 q^{55} + 8 q^{56} - 8 q^{57} + 4 q^{58} + 20 q^{61} + 8 q^{62} + 8 q^{63} - 4 q^{64} - 16 q^{65} + 16 q^{67} + 12 q^{68} - 24 q^{69} + 24 q^{71} - 4 q^{72} + 4 q^{73} - 12 q^{74} + 16 q^{75} - 8 q^{78} - 24 q^{79} - 4 q^{80} - 4 q^{81} + 20 q^{82} - 8 q^{84} + 28 q^{85} - 16 q^{86} - 4 q^{90} - 16 q^{91} - 8 q^{92} - 4 q^{97} - 20 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
102.2.f.a 102.f 17.c $4$ $0.814$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots\)

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

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