Properties

Label 210.2.d
Level 210
Weight 2
Character orbit d
Rep. character \(\chi_{210}(209,\cdot)\)
Character field \(\Q\)
Dimension 16
Newforms 2
Sturm bound 96
Trace bound 2

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Defining parameters

Level: \( N \) = \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 210.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(23\)

Dimensions

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

Total New Old
Modular forms 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

Trace form

\(16q \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 32q^{46} \) \(\mathstrut -\mathstrut 16q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 32q^{70} \) \(\mathstrut -\mathstrut 32q^{79} \) \(\mathstrut +\mathstrut 80q^{81} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut +\mathstrut 64q^{85} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(210, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
210.2.d.a \(8\) \(1.677\) 8.0.\(\cdots\).11 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{7}q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
210.2.d.b \(8\) \(1.677\) 8.0.\(\cdots\).11 None \(8\) \(0\) \(0\) \(0\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)

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

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