Properties

Label 4332.2.a
Level $4332$
Weight $2$
Character orbit 4332.a
Rep. character $\chi_{4332}(1,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $21$
Sturm bound $1520$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 4332 = 2^{2} \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4332.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 21 \)
Sturm bound: \(1520\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4332))\).

Total New Old
Modular forms 820 56 764
Cusp forms 701 56 645
Eisenstein series 119 0 119

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

\(2\)\(3\)\(19\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(13\)
\(-\)\(+\)\(-\)\(+\)\(15\)
\(-\)\(-\)\(+\)\(+\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(18\)
Plus space\(+\)\(25\)
Minus space\(-\)\(31\)

Trace form

\( 56 q - 4 q^{5} - 4 q^{7} + 56 q^{9} + O(q^{10}) \) \( 56 q - 4 q^{5} - 4 q^{7} + 56 q^{9} + 4 q^{11} - 4 q^{15} + 4 q^{23} + 44 q^{25} - 4 q^{29} + 4 q^{31} + 20 q^{35} + 12 q^{37} - 8 q^{39} + 16 q^{41} - 4 q^{43} - 4 q^{45} + 16 q^{47} + 68 q^{49} + 4 q^{51} - 4 q^{53} + 4 q^{55} + 8 q^{59} - 4 q^{63} - 28 q^{65} - 16 q^{67} + 12 q^{69} + 32 q^{71} + 12 q^{73} - 8 q^{75} - 8 q^{77} + 8 q^{79} + 56 q^{81} - 4 q^{83} - 4 q^{85} + 16 q^{87} - 28 q^{89} + 4 q^{91} + 4 q^{93} - 16 q^{97} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4332))\) 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 19
4332.2.a.a 4332.a 1.a $1$ $34.591$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
4332.2.a.b 4332.a 1.a $1$ $34.591$ \(\Q\) None \(0\) \(1\) \(-3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}+q^{7}+q^{9}-5q^{11}+6q^{13}+\cdots\)
4332.2.a.c 4332.a 1.a $1$ $34.591$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
4332.2.a.d 4332.a 1.a $1$ $34.591$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
4332.2.a.e 4332.a 1.a $2$ $34.591$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-1\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta q^{5}-3\beta q^{7}+q^{9}+5q^{11}+\cdots\)
4332.2.a.f 4332.a 1.a $2$ $34.591$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta q^{5}+(-2+4\beta )q^{7}+q^{9}+\cdots\)
4332.2.a.g 4332.a 1.a $2$ $34.591$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
4332.2.a.h 4332.a 1.a $2$ $34.591$ \(\Q(\sqrt{7}) \) None \(0\) \(-2\) \(2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}+(2+\beta )q^{7}+q^{9}+\cdots\)
4332.2.a.i 4332.a 1.a $2$ $34.591$ \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(3\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
4332.2.a.j 4332.a 1.a $2$ $34.591$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-1\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}-3\beta q^{7}+q^{9}+5q^{11}+\cdots\)
4332.2.a.k 4332.a 1.a $2$ $34.591$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}+(-2+4\beta )q^{7}+q^{9}+\cdots\)
4332.2.a.l 4332.a 1.a $2$ $34.591$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
4332.2.a.m 4332.a 1.a $2$ $34.591$ \(\Q(\sqrt{7}) \) None \(0\) \(2\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{5}+(2+\beta )q^{7}+q^{9}+\cdots\)
4332.2.a.n 4332.a 1.a $3$ $34.591$ \(\Q(\zeta_{18})^+\) None \(0\) \(-3\) \(3\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{1}-2\beta _{2})q^{7}+\cdots\)
4332.2.a.o 4332.a 1.a $3$ $34.591$ \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(3\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{1}-2\beta _{2})q^{7}+\cdots\)
4332.2.a.p 4332.a 1.a $4$ $34.591$ \(\Q(\zeta_{20})^+\) None \(0\) \(-4\) \(-4\) \(-6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
4332.2.a.q 4332.a 1.a $4$ $34.591$ 4.4.2225.1 None \(0\) \(-4\) \(-4\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-2\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
4332.2.a.r 4332.a 1.a $4$ $34.591$ \(\Q(\zeta_{20})^+\) None \(0\) \(4\) \(-4\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
4332.2.a.s 4332.a 1.a $4$ $34.591$ 4.4.2225.1 None \(0\) \(4\) \(-4\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-2\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
4332.2.a.t 4332.a 1.a $6$ $34.591$ 6.6.73227321.1 None \(0\) \(-6\) \(3\) \(9\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
4332.2.a.u 4332.a 1.a $6$ $34.591$ 6.6.73227321.1 None \(0\) \(6\) \(3\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4332))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4332)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1444))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2166))\)\(^{\oplus 2}\)