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Properties

Label 105.2.i
Level $105$
Weight $2$
Character orbit 105.i
Rep. character $\chi_{105}(16,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $4$
Sturm bound $32$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(32\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(105, [\chi])\).

Total New Old
Modular forms 40 12 28
Cusp forms 24 12 12
Eisenstein series 16 0 16

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.2.i.a 105.i 7.c $2$ $0.838$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
105.2.i.b 105.i 7.c $2$ $0.838$ \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
105.2.i.c 105.i 7.c $4$ $0.838$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{5}-\beta _{3}q^{6}+\cdots\)
105.2.i.d 105.i 7.c $4$ $0.838$ \(\Q(\zeta_{12})\) None \(2\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)