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Properties

Label 4664.2.a
Level $4664$
Weight $2$
Character orbit 4664.a
Rep. character $\chi_{4664}(1,\cdot)$
Character field $\Q$
Dimension $130$
Newform subspaces $17$
Sturm bound $1296$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4664 = 2^{3} \cdot 11 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4664.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(1296\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4664))\).

Total New Old
Modular forms 656 130 526
Cusp forms 641 130 511
Eisenstein series 15 0 15

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

\(2\)\(11\)\(53\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(15\)
\(+\)\(+\)\(-\)\(-\)\(18\)
\(+\)\(-\)\(+\)\(-\)\(19\)
\(+\)\(-\)\(-\)\(+\)\(13\)
\(-\)\(+\)\(+\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(+\)\(13\)
\(-\)\(-\)\(+\)\(+\)\(15\)
\(-\)\(-\)\(-\)\(-\)\(18\)
Plus space\(+\)\(56\)
Minus space\(-\)\(74\)

Trace form

\( 130 q + 4 q^{3} - 4 q^{5} + 8 q^{7} + 122 q^{9} + O(q^{10}) \) \( 130 q + 4 q^{3} - 4 q^{5} + 8 q^{7} + 122 q^{9} + 8 q^{13} - 16 q^{15} + 8 q^{19} + 24 q^{21} - 20 q^{23} + 130 q^{25} - 8 q^{27} + 24 q^{29} + 28 q^{31} - 4 q^{33} - 40 q^{35} - 8 q^{39} - 8 q^{41} + 16 q^{43} + 12 q^{45} - 4 q^{47} + 106 q^{49} - 24 q^{51} - 6 q^{53} + 44 q^{57} - 24 q^{59} - 16 q^{61} + 16 q^{63} + 48 q^{65} + 12 q^{67} - 4 q^{69} + 20 q^{71} + 8 q^{73} + 4 q^{75} + 56 q^{79} + 178 q^{81} - 40 q^{87} + 24 q^{89} + 88 q^{91} + 8 q^{93} - 56 q^{95} + 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4664))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11 53
4664.2.a.a 4664.a 1.a $1$ $37.242$ \(\Q\) None 4664.2.a.a \(0\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}-2q^{9}-q^{11}-3q^{13}+\cdots\)
4664.2.a.b 4664.a 1.a $1$ $37.242$ \(\Q\) None 4664.2.a.b \(0\) \(-1\) \(3\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-4q^{7}-2q^{9}-q^{11}+\cdots\)
4664.2.a.c 4664.a 1.a $1$ $37.242$ \(\Q\) None 4664.2.a.c \(0\) \(-1\) \(3\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-4q^{7}-2q^{9}+q^{11}+\cdots\)
4664.2.a.d 4664.a 1.a $1$ $37.242$ \(\Q\) None 4664.2.a.d \(0\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}-3q^{9}+q^{11}+6q^{13}+\cdots\)
4664.2.a.e 4664.a 1.a $1$ $37.242$ \(\Q\) None 4664.2.a.e \(0\) \(3\) \(-1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}+4q^{7}+6q^{9}+q^{11}+\cdots\)
4664.2.a.f 4664.a 1.a $2$ $37.242$ \(\Q(\sqrt{2}) \) None 4664.2.a.f \(0\) \(-2\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(2+\beta )q^{7}-2\beta q^{9}+\cdots\)
4664.2.a.g 4664.a 1.a $2$ $37.242$ \(\Q(\sqrt{5}) \) None 4664.2.a.g \(0\) \(2\) \(2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-1-\beta )q^{7}-2q^{9}+q^{11}+\cdots\)
4664.2.a.h 4664.a 1.a $4$ $37.242$ 4.4.53312.1 None 4664.2.a.h \(0\) \(4\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+\cdots\)
4664.2.a.i 4664.a 1.a $5$ $37.242$ 5.5.401584.1 None 4664.2.a.i \(0\) \(3\) \(7\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1+\beta _{1})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
4664.2.a.j 4664.a 1.a $8$ $37.242$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 4664.2.a.j \(0\) \(-4\) \(-3\) \(-7\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-\beta _{5}q^{5}+(-1+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
4664.2.a.k 4664.a 1.a $11$ $37.242$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 4664.2.a.k \(0\) \(-6\) \(3\) \(-5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+\beta _{7}q^{5}-\beta _{10}q^{7}+\cdots\)
4664.2.a.l 4664.a 1.a $13$ $37.242$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 4664.2.a.l \(0\) \(0\) \(-13\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{6})q^{5}-\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
4664.2.a.m 4664.a 1.a $13$ $37.242$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 4664.2.a.m \(0\) \(4\) \(-8\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+\beta _{8}q^{7}+(2+\cdots)q^{9}+\cdots\)
4664.2.a.n 4664.a 1.a $15$ $37.242$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 4664.2.a.n \(0\) \(-3\) \(6\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{10}q^{5}-\beta _{9}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
4664.2.a.o 4664.a 1.a $15$ $37.242$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 4664.2.a.o \(0\) \(-1\) \(-11\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{5})q^{5}-\beta _{10}q^{7}+\cdots\)
4664.2.a.p 4664.a 1.a $18$ $37.242$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 4664.2.a.p \(0\) \(7\) \(-8\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{7}q^{5}+\beta _{5}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
4664.2.a.q 4664.a 1.a $19$ $37.242$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None 4664.2.a.q \(0\) \(0\) \(12\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{10})q^{5}-\beta _{13}q^{7}+(1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4664))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4664)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(106))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(212))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(424))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(583))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1166))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2332))\)\(^{\oplus 2}\)