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Properties

Label 189.4.a
Level $189$
Weight $4$
Character orbit 189.a
Rep. character $\chi_{189}(1,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $12$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 189.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(189))\).

Total New Old
Modular forms 78 24 54
Cusp forms 66 24 42
Eisenstein series 12 0 12

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
\(+\)\(+\)$+$\(7\)
\(+\)\(-\)$-$\(5\)
\(-\)\(+\)$-$\(5\)
\(-\)\(-\)$+$\(7\)
Plus space\(+\)\(14\)
Minus space\(-\)\(10\)

Trace form

\( 24 q + 84 q^{4} + O(q^{10}) \) \( 24 q + 84 q^{4} + 84 q^{10} - 96 q^{13} + 732 q^{16} + 96 q^{22} + 36 q^{25} - 336 q^{28} - 72 q^{31} + 204 q^{34} + 1644 q^{37} + 2184 q^{40} - 252 q^{43} - 1284 q^{46} + 1176 q^{49} - 840 q^{52} - 96 q^{55} - 5220 q^{58} - 3192 q^{61} + 2028 q^{64} + 1308 q^{67} + 252 q^{70} - 3384 q^{73} - 2712 q^{76} + 1680 q^{79} + 1380 q^{82} - 3456 q^{85} + 3744 q^{88} + 420 q^{91} + 3588 q^{94} + 3624 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(189))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7
189.4.a.a 189.a 1.a $1$ $11.151$ \(\Q\) None \(-3\) \(0\) \(12\) \(7\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}+12q^{5}+7q^{7}+21q^{8}+\cdots\)
189.4.a.b 189.a 1.a $1$ $11.151$ \(\Q\) None \(0\) \(0\) \(-21\) \(7\) $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{4}-21q^{5}+7q^{7}+21q^{11}+2q^{13}+\cdots\)
189.4.a.c 189.a 1.a $1$ $11.151$ \(\Q\) None \(0\) \(0\) \(21\) \(7\) $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{4}+21q^{5}+7q^{7}-21q^{11}+2q^{13}+\cdots\)
189.4.a.d 189.a 1.a $1$ $11.151$ \(\Q\) None \(3\) \(0\) \(-12\) \(7\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{2}+q^{4}-12q^{5}+7q^{7}-21q^{8}+\cdots\)
189.4.a.e 189.a 1.a $2$ $11.151$ \(\Q(\sqrt{3}) \) None \(-6\) \(0\) \(-6\) \(14\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-3+\beta )q^{2}+(4-6\beta )q^{4}+(-3+4\beta )q^{5}+\cdots\)
189.4.a.f 189.a 1.a $2$ $11.151$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(14\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-5q^{4}+\beta q^{5}+7q^{7}-13\beta q^{8}+\cdots\)
189.4.a.g 189.a 1.a $2$ $11.151$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(-14\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{4}-\beta q^{5}-7q^{7}-9\beta q^{8}+\cdots\)
189.4.a.h 189.a 1.a $2$ $11.151$ \(\Q(\sqrt{21}) \) None \(0\) \(0\) \(0\) \(14\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+13q^{4}-\beta q^{5}+7q^{7}-5\beta q^{8}+\cdots\)
189.4.a.i 189.a 1.a $2$ $11.151$ \(\Q(\sqrt{3}) \) None \(6\) \(0\) \(6\) \(14\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(3+\beta )q^{2}+(4+6\beta )q^{4}+(3+4\beta )q^{5}+\cdots\)
189.4.a.j 189.a 1.a $3$ $11.151$ 3.3.3576.1 None \(-1\) \(0\) \(-2\) \(-21\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(6-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
189.4.a.k 189.a 1.a $3$ $11.151$ 3.3.3576.1 None \(1\) \(0\) \(2\) \(-21\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(6-2\beta _{1}+\beta _{2})q^{4}+(1+2\beta _{1}+\cdots)q^{5}+\cdots\)
189.4.a.l 189.a 1.a $4$ $11.151$ \(\Q(\sqrt{5}, \sqrt{13})\) None \(0\) \(0\) \(0\) \(-28\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}+(6-\beta _{3})q^{4}+(-4\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(189))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(189)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 2}\)