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Properties

Label 594.2.a
Level $594$
Weight $2$
Character orbit 594.a
Rep. character $\chi_{594}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $10$
Sturm bound $216$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 594 = 2 \cdot 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 594.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(216\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(594))\).

Total New Old
Modular forms 120 12 108
Cusp forms 97 12 85
Eisenstein series 23 0 23

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

\(2\)\(3\)\(11\)FrickeDim
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(-\)$-$\(2\)
\(+\)\(-\)\(+\)$-$\(2\)
\(+\)\(-\)\(-\)$+$\(1\)
\(-\)\(+\)\(+\)$-$\(3\)
\(-\)\(-\)\(-\)$-$\(3\)
Plus space\(+\)\(2\)
Minus space\(-\)\(10\)

Trace form

\( 12 q + 12 q^{4} + 8 q^{7} + O(q^{10}) \) \( 12 q + 12 q^{4} + 8 q^{7} + 16 q^{10} + 24 q^{13} + 12 q^{16} + 20 q^{25} + 8 q^{28} + 12 q^{34} + 12 q^{37} + 16 q^{40} - 8 q^{43} - 8 q^{46} + 24 q^{52} + 4 q^{58} + 16 q^{61} + 12 q^{64} - 24 q^{67} - 24 q^{70} - 16 q^{73} - 40 q^{79} - 4 q^{82} - 24 q^{85} - 40 q^{91} - 32 q^{94} - 20 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(594))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 11
594.2.a.a 594.a 1.a $1$ $4.743$ \(\Q\) None \(-1\) \(0\) \(-3\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-4q^{7}-q^{8}+3q^{10}+\cdots\)
594.2.a.b 594.a 1.a $1$ $4.743$ \(\Q\) None \(-1\) \(0\) \(-2\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
594.2.a.c 594.a 1.a $1$ $4.743$ \(\Q\) None \(-1\) \(0\) \(-2\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\)
594.2.a.d 594.a 1.a $1$ $4.743$ \(\Q\) None \(-1\) \(0\) \(1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots\)
594.2.a.e 594.a 1.a $1$ $4.743$ \(\Q\) None \(1\) \(0\) \(-1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots\)
594.2.a.f 594.a 1.a $1$ $4.743$ \(\Q\) None \(1\) \(0\) \(2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
594.2.a.g 594.a 1.a $1$ $4.743$ \(\Q\) None \(1\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\)
594.2.a.h 594.a 1.a $1$ $4.743$ \(\Q\) None \(1\) \(0\) \(3\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}-4q^{7}+q^{8}+3q^{10}+\cdots\)
594.2.a.i 594.a 1.a $2$ $4.743$ \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(-2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta )q^{5}+2q^{7}-q^{8}+\cdots\)
594.2.a.j 594.a 1.a $2$ $4.743$ \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta )q^{5}+2q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(594))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(594)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(297))\)\(^{\oplus 2}\)