Properties

Label 4592.2.a
Level $4592$
Weight $2$
Character orbit 4592.a
Rep. character $\chi_{4592}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $37$
Sturm bound $1344$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4592 = 2^{4} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4592.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 37 \)
Sturm bound: \(1344\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4592))\).

Total New Old
Modular forms 684 120 564
Cusp forms 661 120 541
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.

\(2\)\(7\)\(41\)FrickeDim
\(+\)\(+\)\(+\)$+$\(15\)
\(+\)\(+\)\(-\)$-$\(15\)
\(+\)\(-\)\(+\)$-$\(15\)
\(+\)\(-\)\(-\)$+$\(15\)
\(-\)\(+\)\(+\)$-$\(18\)
\(-\)\(+\)\(-\)$+$\(11\)
\(-\)\(-\)\(+\)$+$\(12\)
\(-\)\(-\)\(-\)$-$\(19\)
Plus space\(+\)\(53\)
Minus space\(-\)\(67\)

Trace form

\( 120 q + 2 q^{7} + 120 q^{9} + O(q^{10}) \) \( 120 q + 2 q^{7} + 120 q^{9} - 8 q^{11} - 16 q^{15} + 16 q^{19} + 4 q^{23} + 120 q^{25} - 24 q^{27} - 8 q^{29} + 16 q^{31} - 12 q^{35} - 8 q^{37} - 24 q^{39} + 4 q^{43} - 24 q^{47} + 120 q^{49} - 8 q^{51} - 8 q^{53} + 16 q^{57} - 32 q^{61} + 10 q^{63} + 16 q^{65} + 8 q^{67} - 32 q^{69} - 16 q^{71} + 32 q^{75} - 8 q^{77} + 56 q^{79} + 136 q^{81} + 16 q^{83} - 32 q^{85} + 56 q^{87} + 16 q^{89} + 72 q^{95} + 16 q^{97} + 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4592))\) 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 7 41
4592.2.a.a 4592.a 1.a $1$ $36.667$ \(\Q\) None \(0\) \(-3\) \(-1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}-q^{7}+6q^{9}-4q^{11}+\cdots\)
4592.2.a.b 4592.a 1.a $1$ $36.667$ \(\Q\) None \(0\) \(-2\) \(-2\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}+q^{7}+q^{9}+6q^{11}+\cdots\)
4592.2.a.c 4592.a 1.a $1$ $36.667$ \(\Q\) None \(0\) \(-2\) \(2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
4592.2.a.d 4592.a 1.a $1$ $36.667$ \(\Q\) None \(0\) \(-1\) \(-3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-q^{7}-2q^{9}+2q^{13}+\cdots\)
4592.2.a.e 4592.a 1.a $1$ $36.667$ \(\Q\) None \(0\) \(-1\) \(-3\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+q^{7}-2q^{9}-6q^{11}+\cdots\)
4592.2.a.f 4592.a 1.a $1$ $36.667$ \(\Q\) None \(0\) \(0\) \(-4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}-q^{7}-3q^{9}+2q^{11}-6q^{13}+\cdots\)
4592.2.a.g 4592.a 1.a $1$ $36.667$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-3q^{9}+2q^{13}+2q^{17}+\cdots\)
4592.2.a.h 4592.a 1.a $1$ $36.667$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}-2q^{9}+6q^{11}-4q^{13}+\cdots\)
4592.2.a.i 4592.a 1.a $1$ $36.667$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}-2q^{9}-2q^{11}+4q^{13}+\cdots\)
4592.2.a.j 4592.a 1.a $1$ $36.667$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}-2q^{9}+2q^{13}+q^{15}+\cdots\)
4592.2.a.k 4592.a 1.a $1$ $36.667$ \(\Q\) None \(0\) \(2\) \(4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{5}-q^{7}+q^{9}-4q^{11}+\cdots\)
4592.2.a.l 4592.a 1.a $1$ $36.667$ \(\Q\) None \(0\) \(3\) \(-1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}-q^{7}+6q^{9}+2q^{11}+\cdots\)
4592.2.a.m 4592.a 1.a $2$ $36.667$ \(\Q(\sqrt{3}) \) None \(0\) \(-4\) \(2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
4592.2.a.n 4592.a 1.a $2$ $36.667$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
4592.2.a.o 4592.a 1.a $2$ $36.667$ \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(-3\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
4592.2.a.p 4592.a 1.a $2$ $36.667$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
4592.2.a.q 4592.a 1.a $2$ $36.667$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(-1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
4592.2.a.r 4592.a 1.a $3$ $36.667$ \(\Q(\zeta_{14})^+\) None \(0\) \(-5\) \(2\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{3}+(2-2\beta _{1}+2\beta _{2})q^{5}+\cdots\)
4592.2.a.s 4592.a 1.a $3$ $36.667$ 3.3.568.1 None \(0\) \(-1\) \(1\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+q^{7}+(3-2\beta _{1}-\beta _{2})q^{9}+\cdots\)
4592.2.a.t 4592.a 1.a $3$ $36.667$ 3.3.257.1 None \(0\) \(1\) \(6\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{3}+2q^{5}-q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
4592.2.a.u 4592.a 1.a $3$ $36.667$ 3.3.229.1 None \(0\) \(2\) \(-4\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(-1-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
4592.2.a.v 4592.a 1.a $3$ $36.667$ \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(0\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-2\beta _{1}+2\beta _{2})q^{5}-q^{7}+\cdots\)
4592.2.a.w 4592.a 1.a $3$ $36.667$ \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+2\beta _{2}q^{5}+q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
4592.2.a.x 4592.a 1.a $4$ $36.667$ 4.4.6809.1 None \(0\) \(0\) \(-3\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
4592.2.a.y 4592.a 1.a $4$ $36.667$ 4.4.107637.1 None \(0\) \(0\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
4592.2.a.z 4592.a 1.a $4$ $36.667$ 4.4.27329.1 None \(0\) \(1\) \(0\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+(2-2\beta _{1}+\cdots)q^{11}+\cdots\)
4592.2.a.ba 4592.a 1.a $4$ $36.667$ 4.4.11348.1 None \(0\) \(1\) \(3\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
4592.2.a.bb 4592.a 1.a $5$ $36.667$ 5.5.633117.1 None \(0\) \(-4\) \(-5\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
4592.2.a.bc 4592.a 1.a $5$ $36.667$ 5.5.287349.1 None \(0\) \(-2\) \(-3\) \(5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}+q^{7}+\cdots\)
4592.2.a.bd 4592.a 1.a $5$ $36.667$ 5.5.1935333.1 None \(0\) \(-2\) \(3\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{4})q^{5}-q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
4592.2.a.be 4592.a 1.a $5$ $36.667$ 5.5.470117.1 None \(0\) \(2\) \(-1\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+q^{7}+\cdots\)
4592.2.a.bf 4592.a 1.a $6$ $36.667$ 6.6.23279501.1 None \(0\) \(-3\) \(-6\) \(6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1-\beta _{2})q^{5}+q^{7}+\cdots\)
4592.2.a.bg 4592.a 1.a $6$ $36.667$ 6.6.185257757.1 None \(0\) \(4\) \(-1\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{3}+(\beta _{3}-\beta _{4})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
4592.2.a.bh 4592.a 1.a $7$ $36.667$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(4\) \(5\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1+\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
4592.2.a.bi 4592.a 1.a $8$ $36.667$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-3\) \(6\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(1+\beta _{6})q^{5}-q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)
4592.2.a.bj 4592.a 1.a $8$ $36.667$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-3\) \(10\) \(-8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{3}+(1+\beta _{1})q^{5}-q^{7}+(2+\beta _{7})q^{9}+\cdots\)
4592.2.a.bk 4592.a 1.a $9$ $36.667$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-3\) \(-2\) \(9\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+q^{7}+(2+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4592))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4592)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(328))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(574))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(656))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1148))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2296))\)\(^{\oplus 2}\)