↑

Properties

Label 210.2.n
Level $210$
Weight $2$
Character orbit 210.n
Rep. character $\chi_{210}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(210, [\chi])\).

Total New Old
Modular forms 112 16 96
Cusp forms 80 16 64
Eisenstein series 32 0 32

Trace form

\( 16 q + 8 q^{4} - 4 q^{5} + 8 q^{6} + 8 q^{9} + O(q^{10}) \) \( 16 q + 8 q^{4} - 4 q^{5} + 8 q^{6} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{14} + 4 q^{15} - 8 q^{16} + 20 q^{19} - 8 q^{20} + 8 q^{21} + 4 q^{24} - 6 q^{25} - 4 q^{26} - 48 q^{29} + 4 q^{30} + 12 q^{31} - 32 q^{34} - 20 q^{35} + 16 q^{36} + 8 q^{39} + 2 q^{40} - 72 q^{41} - 4 q^{44} + 4 q^{45} - 12 q^{46} + 20 q^{49} + 16 q^{50} - 8 q^{51} + 4 q^{54} + 20 q^{55} - 8 q^{56} - 16 q^{59} + 2 q^{60} - 8 q^{61} - 16 q^{64} - 32 q^{65} - 16 q^{66} - 48 q^{69} - 26 q^{70} + 64 q^{71} + 28 q^{74} - 8 q^{75} + 40 q^{76} + 20 q^{79} - 4 q^{80} - 8 q^{81} + 16 q^{84} + 8 q^{85} + 32 q^{86} + 8 q^{89} - 4 q^{90} + 8 q^{91} + 20 q^{94} + 28 q^{95} - 4 q^{96} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(210, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
210.2.n.a 210.n 35.j $4$ $1.677$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
210.2.n.b 210.n 35.j $12$ $1.677$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(\beta _{2}-\beta _{8})q^{3}+(1+\beta _{10})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(210, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)