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 $1$

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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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
210.2.n.a \(4\) \(1.677\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
210.2.n.b \(12\) \(1.677\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(\beta _{2}-\beta _{8})q^{3}+(1+\beta _{10})q^{4}+\cdots\)

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

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