Properties

Label 189.2.c
Level 189
Weight 2
Character orbit c
Rep. character \(\chi_{189}(188,\cdot)\)
Character field \(\Q\)
Dimension 10
Newforms 3
Sturm bound 48
Trace bound 4

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 189.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(189, [\chi])\).

Total New Old
Modular forms 30 10 20
Cusp forms 18 10 8
Eisenstein series 12 0 12

Trace form

\(10q \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 12q^{16} \) \(\mathstrut -\mathstrut 28q^{22} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 12q^{43} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 29q^{49} \) \(\mathstrut +\mathstrut 80q^{58} \) \(\mathstrut +\mathstrut 36q^{64} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 36q^{70} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut 36q^{85} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 27q^{91} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(189, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
189.2.c.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(q+2q^{4}+\zeta_{6}q^{7}+(1-2\zeta_{6})q^{13}+4q^{16}+\cdots\)
189.2.c.b \(4\) \(1.509\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{1}q^{2}-3q^{4}-\beta _{3}q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
189.2.c.c \(4\) \(1.509\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{2}-\beta _{2}q^{5}+(1-\beta _{3})q^{7}-2\beta _{1}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(189, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(189, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)