Properties

Label 1890.2.k
Level 1890
Weight 2
Character orbit k
Rep. character \(\chi_{1890}(541,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 88
Newforms 38
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.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 38 \)
Sturm bound: \(864\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(23\)

Dimensions

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

Total New Old
Modular forms 912 88 824
Cusp forms 816 88 728
Eisenstein series 96 0 96

Trace form

\(88q \) \(\mathstrut -\mathstrut 44q^{4} \) \(\mathstrut +\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(88q \) \(\mathstrut -\mathstrut 44q^{4} \) \(\mathstrut +\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 44q^{16} \) \(\mathstrut -\mathstrut 24q^{19} \) \(\mathstrut -\mathstrut 44q^{25} \) \(\mathstrut -\mathstrut 12q^{28} \) \(\mathstrut +\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 8q^{49} \) \(\mathstrut +\mathstrut 12q^{52} \) \(\mathstrut +\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{61} \) \(\mathstrut +\mathstrut 88q^{64} \) \(\mathstrut +\mathstrut 36q^{67} \) \(\mathstrut -\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 48q^{76} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut -\mathstrut 104q^{91} \) \(\mathstrut +\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 24q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.k.a \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1890.2.k.b \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.c \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1890.2.k.d \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1890.2.k.e \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1890.2.k.f \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1890.2.k.g \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.h \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1890.2.k.i \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1890.2.k.j \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.k \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.l \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.m \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.n \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.o \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1890.2.k.p \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.q \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.r \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1890.2.k.s \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1890.2.k.t \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1890.2.k.u \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.v \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.w \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.x \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.y \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.z \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.ba \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1890.2.k.bb \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1890.2.k.bc \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(-4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.bd \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1890.2.k.be \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1890.2.k.bf \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1890.2.k.bg \(4\) \(15.092\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(-2\) \(-2\) \(q+(-1-\beta _{1})q^{2}+\beta _{1}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1890.2.k.bh \(4\) \(15.092\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-2\) \(0\) \(-2\) \(0\) \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+\beta _{2}q^{5}+\beta _{1}q^{7}+\cdots\)
1890.2.k.bi \(4\) \(15.092\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-2\) \(0\) \(-2\) \(10\) \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+\beta _{2}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.bj \(4\) \(15.092\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(2\) \(-2\) \(q+(1+\beta _{1})q^{2}+\beta _{1}q^{4}+(1+\beta _{1})q^{5}+\cdots\)
1890.2.k.bk \(4\) \(15.092\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(2\) \(0\) \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}-\beta _{2}q^{5}-\beta _{1}q^{7}+\cdots\)
1890.2.k.bl \(4\) \(15.092\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(2\) \(10\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(1+\beta _{2})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(945, [\chi])\)\(^{\oplus 2}\)