Properties

Label 4608.2.a
Level $4608$
Weight $2$
Character orbit 4608.a
Rep. character $\chi_{4608}(1,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $29$
Sturm bound $1536$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 4608 = 2^{9} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4608.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 29 \)
Sturm bound: \(1536\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4608))\).

Total New Old
Modular forms 832 80 752
Cusp forms 705 80 625
Eisenstein series 127 0 127

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

\(2\)\(3\)FrickeDim.
\(+\)\(+\)\(+\)\(16\)
\(+\)\(-\)\(-\)\(26\)
\(-\)\(+\)\(-\)\(16\)
\(-\)\(-\)\(+\)\(22\)
Plus space\(+\)\(38\)
Minus space\(-\)\(42\)

Trace form

\( 80 q + O(q^{10}) \) \( 80 q + 80 q^{25} + 80 q^{49} - 32 q^{65} - 32 q^{73} - 32 q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4608))\) 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
4608.2.a.a 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}+(-2-\beta )q^{7}+2q^{11}+\cdots\)
4608.2.a.b 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}-\beta q^{7}+(-2+2\beta )q^{11}+\cdots\)
4608.2.a.c 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+2\beta q^{7}+3\beta q^{11}+6q^{13}+\cdots\)
4608.2.a.d 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}+\beta q^{7}+(2-2\beta )q^{11}+\cdots\)
4608.2.a.e 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}+(2+\beta )q^{7}-2q^{11}+\cdots\)
4608.2.a.f 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2\beta q^{5}-4q^{7}-\beta q^{11}+2\beta q^{13}+\cdots\)
4608.2.a.g 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-3\beta q^{7}-6q^{11}-4\beta q^{13}+\cdots\)
4608.2.a.h 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-\beta q^{7}-2q^{11}-2q^{17}+4q^{19}+\cdots\)
4608.2.a.i 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $+$ $-$ $N(\mathrm{U}(1))$ \(q+(-2+3\beta )q^{11}+4\beta q^{17}+(6-\beta )q^{19}+\cdots\)
4608.2.a.j 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+\beta q^{7}+2q^{11}-2q^{17}-4q^{19}+\cdots\)
4608.2.a.k 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+(2-3\beta )q^{11}+4\beta q^{17}+(-6+\beta )q^{19}+\cdots\)
4608.2.a.l 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+3\beta q^{7}+6q^{11}-4\beta q^{13}+\cdots\)
4608.2.a.m 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2\beta q^{5}+4q^{7}+\beta q^{11}+2\beta q^{13}+\cdots\)
4608.2.a.n 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+(-2+\beta )q^{7}-2q^{11}+\cdots\)
4608.2.a.o 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}-\beta q^{7}+(-2-2\beta )q^{11}+\cdots\)
4608.2.a.p 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2\beta q^{7}-3\beta q^{11}-6q^{13}+\cdots\)
4608.2.a.q 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+\beta q^{7}+(2+2\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
4608.2.a.r 4608.a 1.a $2$ $36.795$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+(2-\beta )q^{7}+2q^{11}+2\beta q^{13}+\cdots\)
4608.2.a.s 4608.a 1.a $4$ $36.795$ \(\Q(\zeta_{24})^+\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(-8\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q+(-2-\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}-\beta _{3}q^{11}+\cdots\)
4608.2.a.t 4608.a 1.a $4$ $36.795$ 4.4.4352.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(-2-\beta _{2})q^{11}+\cdots\)
4608.2.a.u 4608.a 1.a $4$ $36.795$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}-\beta _{1}q^{7}-2q^{11}-\beta _{2}q^{13}+\cdots\)
4608.2.a.v 4608.a 1.a $4$ $36.795$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}-2\beta _{2}q^{13}+\cdots\)
4608.2.a.w 4608.a 1.a $4$ $36.795$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+\beta _{3}q^{7}+\beta _{1}q^{11}+\beta _{2}q^{13}+\cdots\)
4608.2.a.x 4608.a 1.a $4$ $36.795$ \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}-\beta _{2}q^{7}+\beta _{3}q^{11}-\beta _{3}q^{13}+\cdots\)
4608.2.a.y 4608.a 1.a $4$ $36.795$ \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}-\beta _{3}q^{13}+\cdots\)
4608.2.a.z 4608.a 1.a $4$ $36.795$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}+2\beta _{2}q^{13}+\cdots\)
4608.2.a.ba 4608.a 1.a $4$ $36.795$ 4.4.4352.1 None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+\beta _{3}q^{7}+(2+\beta _{2})q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
4608.2.a.bb 4608.a 1.a $4$ $36.795$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+\beta _{1}q^{7}+2q^{11}-\beta _{2}q^{13}+\cdots\)
4608.2.a.bc 4608.a 1.a $4$ $36.795$ \(\Q(\zeta_{24})^+\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(8\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+(2+\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4608))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4608)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(512))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(768))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1536))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2304))\)\(^{\oplus 2}\)