Properties

Label 1890.2.a
Level 1890
Weight 2
Character orbit a
Rep. character \(\chi_{1890}(1,\cdot)\)
Character field \(\Q\)
Dimension 32
Newforms 28
Sturm bound 864
Trace bound 13

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Defining parameters

Level: \( N \) = \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1890.a (trivial)
Character field: \(\Q\)
Newforms: \( 28 \)
Sturm bound: \(864\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1890))\).

Total New Old
Modular forms 456 32 424
Cusp forms 409 32 377
Eisenstein series 47 0 47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(12\)
Minus space\(-\)\(20\)

Trace form

\(32q \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 32q^{16} \) \(\mathstrut +\mathstrut 32q^{25} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 16q^{46} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 24q^{58} \) \(\mathstrut +\mathstrut 32q^{61} \) \(\mathstrut +\mathstrut 32q^{64} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 32q^{82} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 40q^{94} \) \(\mathstrut -\mathstrut 96q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1890))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 7
1890.2.a.a \(1\) \(15.092\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
1890.2.a.b \(1\) \(15.092\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
1890.2.a.c \(1\) \(15.092\) \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
1890.2.a.d \(1\) \(15.092\) \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
1890.2.a.e \(1\) \(15.092\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
1890.2.a.f \(1\) \(15.092\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
1890.2.a.g \(1\) \(15.092\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
1890.2.a.h \(1\) \(15.092\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
1890.2.a.i \(1\) \(15.092\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
1890.2.a.j \(1\) \(15.092\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
1890.2.a.k \(1\) \(15.092\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
1890.2.a.l \(1\) \(15.092\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
1890.2.a.m \(1\) \(15.092\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
1890.2.a.n \(1\) \(15.092\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
1890.2.a.o \(1\) \(15.092\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
1890.2.a.p \(1\) \(15.092\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
1890.2.a.q \(1\) \(15.092\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
1890.2.a.r \(1\) \(15.092\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
1890.2.a.s \(1\) \(15.092\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
1890.2.a.t \(1\) \(15.092\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
1890.2.a.u \(1\) \(15.092\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1890.2.a.v \(1\) \(15.092\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1890.2.a.w \(1\) \(15.092\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
1890.2.a.x \(1\) \(15.092\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
1890.2.a.y \(2\) \(15.092\) \(\Q(\sqrt{97}) \) None \(-2\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
1890.2.a.z \(2\) \(15.092\) \(\Q(\sqrt{73}) \) None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
1890.2.a.ba \(2\) \(15.092\) \(\Q(\sqrt{97}) \) None \(2\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1890.2.a.bb \(2\) \(15.092\) \(\Q(\sqrt{73}) \) None \(2\) \(0\) \(2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1890))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1890)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(945))\)\(^{\oplus 2}\)