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Properties

Label 103.2.c
Level $103$
Weight $2$
Character orbit 103.c
Rep. character $\chi_{103}(46,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $1$
Sturm bound $17$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 103.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 103 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(17\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(103, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 16 16 0
Eisenstein series 4 4 0

Trace form

\( 16 q - q^{2} - 4 q^{3} - 9 q^{4} + 3 q^{5} - 3 q^{6} - 5 q^{7} + 6 q^{8} + 8 q^{9} + O(q^{10}) \) \( 16 q - q^{2} - 4 q^{3} - 9 q^{4} + 3 q^{5} - 3 q^{6} - 5 q^{7} + 6 q^{8} + 8 q^{9} - 16 q^{10} - 2 q^{11} + 16 q^{12} - 8 q^{13} - 6 q^{14} - 3 q^{15} - 3 q^{16} - 18 q^{18} + 8 q^{19} + 9 q^{20} + 15 q^{21} + 28 q^{22} - 18 q^{23} - 42 q^{24} + 5 q^{25} + 20 q^{26} - 34 q^{27} + 16 q^{28} - 9 q^{29} + 48 q^{30} - 14 q^{31} + 3 q^{32} - 15 q^{33} + 22 q^{34} + 7 q^{35} - 24 q^{36} + 18 q^{37} + 2 q^{38} - 14 q^{39} + 5 q^{40} - 2 q^{41} + 8 q^{42} - 8 q^{43} - 23 q^{44} - 14 q^{45} - 24 q^{46} + 23 q^{47} + 12 q^{48} - 31 q^{49} + 26 q^{50} + 38 q^{51} + 11 q^{52} - 13 q^{53} + 19 q^{54} + 32 q^{55} - 20 q^{56} - 6 q^{57} - 6 q^{58} + 9 q^{59} - 8 q^{60} - 28 q^{61} - 17 q^{62} - 56 q^{63} + 10 q^{64} + q^{65} - 48 q^{66} + 13 q^{67} + 19 q^{68} + 34 q^{69} + 10 q^{70} + 6 q^{71} + 80 q^{72} + 34 q^{73} + 39 q^{74} + 14 q^{75} - 46 q^{76} + 21 q^{77} - 52 q^{78} + 8 q^{79} - 44 q^{80} + 48 q^{81} - 3 q^{82} - 6 q^{83} + 65 q^{84} - 2 q^{85} + 29 q^{86} + 21 q^{87} - 57 q^{88} - 76 q^{89} - 118 q^{90} + 30 q^{91} + 51 q^{92} + 92 q^{93} - 64 q^{94} + 18 q^{95} + 39 q^{96} - 8 q^{97} - 2 q^{98} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(103, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
103.2.c.a 103.c 103.c $16$ $0.822$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-1\) \(-4\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+\beta _{12}q^{3}+(-1+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)