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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.2.i.a \(2\) \(0.838\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(5\) \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
105.2.i.b \(2\) \(0.838\) \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(-1\) \(-1\) \(q+2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
105.2.i.c \(4\) \(0.838\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(2\) \(-2\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{5}-\beta _{3}q^{6}+\cdots\)
105.2.i.d \(4\) \(0.838\) \(\Q(\zeta_{12})\) None \(2\) \(2\) \(-2\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)