Properties

Label 10.3.c
Level $10$
Weight $3$
Character orbit 10.c
Rep. character $\chi_{10}(3,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $2$
Newform subspaces $1$
Sturm bound $4$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 10.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(10, [\chi])\).

Total New Old
Modular forms 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

Trace form

\( 2 q - 2 q^{2} - 4 q^{3} + 8 q^{6} + 4 q^{7} + 4 q^{8} + O(q^{10}) \) \( 2 q - 2 q^{2} - 4 q^{3} + 8 q^{6} + 4 q^{7} + 4 q^{8} - 10 q^{10} - 16 q^{11} - 8 q^{12} + 6 q^{13} + 20 q^{15} - 8 q^{16} + 14 q^{17} + 2 q^{18} + 20 q^{20} - 16 q^{21} + 16 q^{22} - 4 q^{23} - 50 q^{25} - 12 q^{26} - 40 q^{27} - 8 q^{28} + 104 q^{31} + 8 q^{32} + 32 q^{33} + 20 q^{35} - 4 q^{36} - 6 q^{37} - 40 q^{38} - 20 q^{40} - 16 q^{41} + 16 q^{42} - 84 q^{43} + 10 q^{45} + 8 q^{46} - 36 q^{47} + 16 q^{48} + 50 q^{50} - 56 q^{51} + 12 q^{52} + 106 q^{53} + 16 q^{56} + 80 q^{57} + 80 q^{58} - 40 q^{60} - 96 q^{61} - 104 q^{62} - 4 q^{63} - 30 q^{65} - 64 q^{66} + 124 q^{67} - 28 q^{68} - 40 q^{70} - 56 q^{71} + 4 q^{72} - 94 q^{73} + 100 q^{75} + 80 q^{76} - 32 q^{77} + 24 q^{78} + 142 q^{81} + 16 q^{82} + 36 q^{83} + 70 q^{85} + 168 q^{86} - 160 q^{87} - 32 q^{88} - 10 q^{90} + 24 q^{91} - 8 q^{92} - 208 q^{93} - 200 q^{95} - 32 q^{96} - 126 q^{97} - 82 q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
10.3.c.a 10.c 5.c $2$ $0.272$ \(\Q(\sqrt{-1}) \) None 10.3.c.a \(-2\) \(-4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots\)