Properties

Label 210.2.t
Level $210$
Weight $2$
Character orbit 210.t
Rep. character $\chi_{210}(59,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $6$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(11\), \(13\), \(23\)

Dimensions

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

Total New Old
Modular forms 112 32 80
Cusp forms 80 32 48
Eisenstein series 32 0 32

Trace form

\( 32q - 16q^{4} + 6q^{9} + O(q^{10}) \) \( 32q - 16q^{4} + 6q^{9} - 6q^{10} + 20q^{15} - 16q^{16} - 24q^{19} + 10q^{21} - 6q^{24} + 6q^{25} - 10q^{30} - 12q^{31} - 12q^{36} - 12q^{39} + 6q^{40} + 6q^{45} - 4q^{46} + 40q^{49} - 4q^{51} - 10q^{60} - 60q^{61} + 32q^{64} + 48q^{66} - 10q^{70} - 96q^{75} - 52q^{79} + 22q^{81} + 16q^{84} - 88q^{85} + 16q^{91} + 96q^{94} + 6q^{96} + 32q^{99} + O(q^{100}) \)

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.t.a \(4\) \(1.677\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(-2\) \(-6\) \(-10\) \(q+(-1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
210.2.t.b \(4\) \(1.677\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(-1\) \(-3\) \(10\) \(q+(-1+\beta _{2})q^{2}-\beta _{1}q^{3}-\beta _{2}q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\)
210.2.t.c \(4\) \(1.677\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(1\) \(6\) \(-10\) \(q+\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
210.2.t.d \(4\) \(1.677\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(2\) \(3\) \(10\) \(q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
210.2.t.e \(8\) \(1.677\) 8.0.3317760000.3 None \(-4\) \(0\) \(12\) \(0\) \(q-\beta _{4}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
210.2.t.f \(8\) \(1.677\) 8.0.3317760000.3 None \(4\) \(0\) \(-12\) \(0\) \(q+\beta _{4}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)

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

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