Properties

Label 189.2.a
Level $189$
Weight $2$
Character orbit 189.a
Rep. character $\chi_{189}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $6$
Sturm bound $48$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(48\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(189))\).

Total New Old
Modular forms 30 8 22
Cusp forms 19 8 11
Eisenstein series 11 0 11

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

\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(6\)

Trace form

\( 8q + 12q^{4} + O(q^{10}) \) \( 8q + 12q^{4} - 4q^{10} - 12q^{13} + 12q^{16} + 12q^{19} - 4q^{22} - 16q^{28} + 20q^{31} - 36q^{34} - 40q^{37} - 48q^{40} + 28q^{43} - 12q^{46} + 8q^{49} - 8q^{52} + 52q^{55} + 8q^{58} - 12q^{61} - 4q^{64} + 16q^{70} + 8q^{73} + 40q^{76} + 4q^{79} + 28q^{82} - 12q^{85} - 36q^{88} + 4q^{91} - 12q^{94} - 28q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(189))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7
189.2.a.a \(1\) \(1.509\) \(\Q\) None \(-2\) \(0\) \(-1\) \(-1\) \(+\) \(+\) \(q-2q^{2}+2q^{4}-q^{5}-q^{7}+2q^{10}+\cdots\)
189.2.a.b \(1\) \(1.509\) \(\Q\) None \(0\) \(0\) \(-3\) \(1\) \(-\) \(-\) \(q-2q^{4}-3q^{5}+q^{7}-6q^{11}-4q^{13}+\cdots\)
189.2.a.c \(1\) \(1.509\) \(\Q\) None \(0\) \(0\) \(3\) \(1\) \(+\) \(-\) \(q-2q^{4}+3q^{5}+q^{7}+6q^{11}-4q^{13}+\cdots\)
189.2.a.d \(1\) \(1.509\) \(\Q\) None \(2\) \(0\) \(1\) \(-1\) \(-\) \(+\) \(q+2q^{2}+2q^{4}+q^{5}-q^{7}+2q^{10}+\cdots\)
189.2.a.e \(2\) \(1.509\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(q+\beta q^{2}+q^{4}+\beta q^{5}+q^{7}-\beta q^{8}+3q^{10}+\cdots\)
189.2.a.f \(2\) \(1.509\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(q+\beta q^{2}+5q^{4}-\beta q^{5}-q^{7}+3\beta q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(189))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(189)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 2}\)