Properties

Label 1890.2.d
Level 1890
Weight 2
Character orbit d
Rep. character \(\chi_{1890}(1889,\cdot)\)
Character field \(\Q\)
Dimension 64
Newforms 6
Sturm bound 864
Trace bound 23

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Defining parameters

Level: \( N \) = \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1890.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(864\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(11\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1890, [\chi])\).

Total New Old
Modular forms 456 64 392
Cusp forms 408 64 344
Eisenstein series 48 0 48

Trace form

\(64q \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 68q^{49} \) \(\mathstrut +\mathstrut 64q^{64} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut +\mathstrut 64q^{79} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1890, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1890.2.d.a \(8\) \(15.092\) 8.0.303595776.1 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+(-\beta _{3}-\beta _{5}+\beta _{7})q^{5}+\cdots\)
1890.2.d.b \(8\) \(15.092\) 8.0.\(\cdots\).2 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
1890.2.d.c \(8\) \(15.092\) 8.0.\(\cdots\).2 None \(8\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+(\beta _{1}-\beta _{3})q^{5}-\beta _{4}q^{7}+\cdots\)
1890.2.d.d \(8\) \(15.092\) 8.0.303595776.1 None \(8\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+(\beta _{1}+\beta _{3}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1890.2.d.e \(16\) \(15.092\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-\beta _{15}q^{5}-\beta _{6}q^{7}-q^{8}+\cdots\)
1890.2.d.f \(16\) \(15.092\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta _{8}q^{5}-\beta _{11}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1890, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(945, [\chi])\)\(^{\oplus 2}\)