Properties

Label 70.2.e
Level $70$
Weight $2$
Character orbit 70.e
Rep. character $\chi_{70}(11,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $4$
Sturm bound $24$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 70.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(24\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(70, [\chi])\).

Total New Old
Modular forms 32 8 24
Cusp forms 16 8 8
Eisenstein series 16 0 16

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(70, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
70.2.e.a $2$ $0.559$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(1\) \(1\) \(q-\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
70.2.e.b $2$ $0.559$ \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(1\) \(-4\) \(q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
70.2.e.c $2$ $0.559$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
70.2.e.d $2$ $0.559$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-1\) \(-4\) \(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(70, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(70, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)