Properties

Label 1472.4.a
Level $1472$
Weight $4$
Character orbit 1472.a
Rep. character $\chi_{1472}(1,\cdot)$
Character field $\Q$
Dimension $132$
Newform subspaces $38$
Sturm bound $768$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1472 = 2^{6} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1472.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 38 \)
Sturm bound: \(768\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1472))\).

Total New Old
Modular forms 588 132 456
Cusp forms 564 132 432
Eisenstein series 24 0 24

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

\(2\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(34\)
\(+\)\(-\)\(-\)\(31\)
\(-\)\(+\)\(-\)\(32\)
\(-\)\(-\)\(+\)\(35\)
Plus space\(+\)\(69\)
Minus space\(-\)\(63\)

Trace form

\( 132 q + 1188 q^{9} + O(q^{10}) \) \( 132 q + 1188 q^{9} - 144 q^{13} + 104 q^{17} + 240 q^{21} + 3212 q^{25} + 464 q^{33} + 1008 q^{37} - 392 q^{41} + 6468 q^{49} - 688 q^{57} + 2160 q^{61} - 1536 q^{65} - 296 q^{73} + 8852 q^{81} + 88 q^{89} + 5832 q^{93} + 1160 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1472))\) 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 23
1472.4.a.a 1472.a 1.a $1$ $86.851$ \(\Q\) None 46.4.a.b \(0\) \(-9\) \(20\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-9q^{3}+20q^{5}-2q^{7}+54q^{9}-52q^{11}+\cdots\)
1472.4.a.b 1472.a 1.a $1$ $86.851$ \(\Q\) None 184.4.a.b \(0\) \(-8\) \(4\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-8q^{3}+4q^{5}-4q^{7}+37q^{9}-26q^{11}+\cdots\)
1472.4.a.c 1472.a 1.a $1$ $86.851$ \(\Q\) None 23.4.a.a \(0\) \(-5\) \(6\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{3}+6q^{5}+8q^{7}-2q^{9}+34q^{11}+\cdots\)
1472.4.a.d 1472.a 1.a $1$ $86.851$ \(\Q\) None 184.4.a.a \(0\) \(-4\) \(-22\) \(-8\) $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{3}-22q^{5}-8q^{7}-11q^{9}-20q^{11}+\cdots\)
1472.4.a.e 1472.a 1.a $1$ $86.851$ \(\Q\) None 46.4.a.a \(0\) \(-1\) \(10\) \(12\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+10q^{5}+12q^{7}-26q^{9}-42q^{11}+\cdots\)
1472.4.a.f 1472.a 1.a $1$ $86.851$ \(\Q\) None 46.4.a.a \(0\) \(1\) \(10\) \(-12\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+10q^{5}-12q^{7}-26q^{9}+42q^{11}+\cdots\)
1472.4.a.g 1472.a 1.a $1$ $86.851$ \(\Q\) None 184.4.a.a \(0\) \(4\) \(-22\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{3}-22q^{5}+8q^{7}-11q^{9}+20q^{11}+\cdots\)
1472.4.a.h 1472.a 1.a $1$ $86.851$ \(\Q\) None 23.4.a.a \(0\) \(5\) \(6\) \(-8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+5q^{3}+6q^{5}-8q^{7}-2q^{9}-34q^{11}+\cdots\)
1472.4.a.i 1472.a 1.a $1$ $86.851$ \(\Q\) None 184.4.a.b \(0\) \(8\) \(4\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+8q^{3}+4q^{5}+4q^{7}+37q^{9}+26q^{11}+\cdots\)
1472.4.a.j 1472.a 1.a $1$ $86.851$ \(\Q\) None 46.4.a.b \(0\) \(9\) \(20\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+9q^{3}+20q^{5}+2q^{7}+54q^{9}+52q^{11}+\cdots\)
1472.4.a.k 1472.a 1.a $2$ $86.851$ \(\Q(\sqrt{73}) \) None 46.4.a.d \(0\) \(-3\) \(-10\) \(12\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-6+2\beta )q^{5}+(8-4\beta )q^{7}+\cdots\)
1472.4.a.l 1472.a 1.a $2$ $86.851$ \(\Q(\sqrt{41}) \) None 46.4.a.c \(0\) \(-1\) \(-10\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-3\beta )q^{3}+(-4-2\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
1472.4.a.m 1472.a 1.a $2$ $86.851$ \(\Q(\sqrt{41}) \) None 46.4.a.c \(0\) \(1\) \(-10\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+3\beta )q^{3}+(-4-2\beta )q^{5}+(2+\cdots)q^{7}+\cdots\)
1472.4.a.n 1472.a 1.a $2$ $86.851$ \(\Q(\sqrt{73}) \) None 46.4.a.d \(0\) \(3\) \(-10\) \(-12\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-6+2\beta )q^{5}+(-8+4\beta )q^{7}+\cdots\)
1472.4.a.o 1472.a 1.a $3$ $86.851$ 3.3.28669.1 None 92.4.a.b \(0\) \(-8\) \(0\) \(42\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-3-\beta _{2})q^{3}-\beta _{1}q^{5}+(14-\beta _{1}+\cdots)q^{7}+\cdots\)
1472.4.a.p 1472.a 1.a $3$ $86.851$ 3.3.1229.1 None 92.4.a.a \(0\) \(-4\) \(10\) \(46\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(4+\beta _{1}-3\beta _{2})q^{5}+\cdots\)
1472.4.a.q 1472.a 1.a $3$ $86.851$ 3.3.761.1 None 184.4.a.c \(0\) \(-3\) \(-2\) \(28\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
1472.4.a.r 1472.a 1.a $3$ $86.851$ 3.3.11032.1 None 736.4.a.a \(0\) \(-2\) \(0\) \(-16\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-4+\cdots)q^{7}+\cdots\)
1472.4.a.s 1472.a 1.a $3$ $86.851$ 3.3.761.1 None 184.4.a.d \(0\) \(-1\) \(-16\) \(18\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-5-2\beta _{1}-\beta _{2})q^{5}+(5+\cdots)q^{7}+\cdots\)
1472.4.a.t 1472.a 1.a $3$ $86.851$ 3.3.761.1 None 184.4.a.d \(0\) \(1\) \(-16\) \(-18\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-5-2\beta _{1}-\beta _{2})q^{5}+(-5+\cdots)q^{7}+\cdots\)
1472.4.a.u 1472.a 1.a $3$ $86.851$ 3.3.11032.1 None 736.4.a.a \(0\) \(2\) \(0\) \(16\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(4+3\beta _{1}+\cdots)q^{7}+\cdots\)
1472.4.a.v 1472.a 1.a $3$ $86.851$ 3.3.761.1 None 184.4.a.c \(0\) \(3\) \(-2\) \(-28\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
1472.4.a.w 1472.a 1.a $3$ $86.851$ 3.3.1229.1 None 92.4.a.a \(0\) \(4\) \(10\) \(-46\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(4+\beta _{1}-3\beta _{2})q^{5}+(-18+\cdots)q^{7}+\cdots\)
1472.4.a.x 1472.a 1.a $3$ $86.851$ 3.3.28669.1 None 92.4.a.b \(0\) \(8\) \(0\) \(-42\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(3+\beta _{2})q^{3}-\beta _{1}q^{5}+(-14+\beta _{1}+\cdots)q^{7}+\cdots\)
1472.4.a.y 1472.a 1.a $4$ $86.851$ 4.4.334189.1 None 23.4.a.b \(0\) \(-7\) \(-14\) \(16\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{3}+(-3-\beta _{1}+\beta _{3})q^{5}+\cdots\)
1472.4.a.z 1472.a 1.a $4$ $86.851$ 4.4.2822449.1 None 184.4.a.f \(0\) \(-5\) \(2\) \(-32\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1+\beta _{1}-\beta _{3})q^{5}+\cdots\)
1472.4.a.ba 1472.a 1.a $4$ $86.851$ 4.4.167313.1 None 184.4.a.e \(0\) \(-1\) \(20\) \(-10\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(5-\beta _{2}-\beta _{3})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
1472.4.a.bb 1472.a 1.a $4$ $86.851$ 4.4.310848.1 None 736.4.a.c \(0\) \(0\) \(20\) \(-44\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(5-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-11+\cdots)q^{7}+\cdots\)
1472.4.a.bc 1472.a 1.a $4$ $86.851$ 4.4.310848.1 None 736.4.a.c \(0\) \(0\) \(20\) \(44\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(5-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(11+\cdots)q^{7}+\cdots\)
1472.4.a.bd 1472.a 1.a $4$ $86.851$ 4.4.167313.1 None 184.4.a.e \(0\) \(1\) \(20\) \(10\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(5-\beta _{2}-\beta _{3})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
1472.4.a.be 1472.a 1.a $4$ $86.851$ 4.4.2822449.1 None 184.4.a.f \(0\) \(5\) \(2\) \(32\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1+\beta _{1}-\beta _{3})q^{5}+(8+\cdots)q^{7}+\cdots\)
1472.4.a.bf 1472.a 1.a $4$ $86.851$ 4.4.334189.1 None 23.4.a.b \(0\) \(7\) \(-14\) \(-16\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta _{2})q^{3}+(-3-\beta _{1}+\beta _{3})q^{5}+\cdots\)
1472.4.a.bg 1472.a 1.a $8$ $86.851$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 736.4.a.e \(0\) \(-12\) \(12\) \(-14\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}+(1+\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1472.4.a.bh 1472.a 1.a $8$ $86.851$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 736.4.a.e \(0\) \(12\) \(12\) \(14\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{3}+(1+\beta _{3})q^{5}+(2-\beta _{7})q^{7}+\cdots\)
1472.4.a.bi 1472.a 1.a $9$ $86.851$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 736.4.a.g \(0\) \(-14\) \(-30\) \(-28\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}+(-3+\beta _{4})q^{5}+(-3+\cdots)q^{7}+\cdots\)
1472.4.a.bj 1472.a 1.a $9$ $86.851$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 736.4.a.h \(0\) \(0\) \(0\) \(-42\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+\beta _{5}q^{5}+(-5+\beta _{3})q^{7}+(8+\cdots)q^{9}+\cdots\)
1472.4.a.bk 1472.a 1.a $9$ $86.851$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 736.4.a.h \(0\) \(0\) \(0\) \(42\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+\beta _{5}q^{5}+(5-\beta _{3})q^{7}+(8-\beta _{3}+\cdots)q^{9}+\cdots\)
1472.4.a.bl 1472.a 1.a $9$ $86.851$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 736.4.a.g \(0\) \(14\) \(-30\) \(28\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{3}+(-3+\beta _{4})q^{5}+(3-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1472))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1472)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(736))\)\(^{\oplus 2}\)