Properties

Label 1890.2.t
Level 1890
Weight 2
Character orbit t
Rep. character \(\chi_{1890}(1151,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 64
Newforms 3
Sturm bound 864
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1890.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 3 \)
Sturm bound: \(864\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

Total New Old
Modular forms 912 64 848
Cusp forms 816 64 752
Eisenstein series 96 0 96

Trace form

\(64q \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 32q^{16} \) \(\mathstrut +\mathstrut 64q^{25} \) \(\mathstrut -\mathstrut 24q^{26} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut -\mathstrut 8q^{49} \) \(\mathstrut +\mathstrut 72q^{53} \) \(\mathstrut +\mathstrut 60q^{59} \) \(\mathstrut +\mathstrut 102q^{61} \) \(\mathstrut -\mathstrut 64q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 28q^{67} \) \(\mathstrut -\mathstrut 6q^{70} \) \(\mathstrut +\mathstrut 12q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 12q^{85} \) \(\mathstrut -\mathstrut 6q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 36q^{92} \) \(\mathstrut +\mathstrut 12q^{97} \) \(\mathstrut +\mathstrut 48q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.t.a \(4\) \(15.092\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(2\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1890.2.t.b \(28\) \(15.092\) None \(0\) \(0\) \(28\) \(-4\)
1890.2.t.c \(32\) \(15.092\) None \(0\) \(0\) \(-32\) \(-2\)

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

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(945, [\chi])\)\(^{\oplus 2}\)