Properties

Label 832.4.a
Level $832$
Weight $4$
Character orbit 832.a
Rep. character $\chi_{832}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $35$
Sturm bound $448$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 832.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 35 \)
Sturm bound: \(448\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(832))\).

Total New Old
Modular forms 348 72 276
Cusp forms 324 72 252
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.

\(2\)\(13\)FrickeDim
\(+\)\(+\)\(+\)\(19\)
\(+\)\(-\)\(-\)\(17\)
\(-\)\(+\)\(-\)\(17\)
\(-\)\(-\)\(+\)\(19\)
Plus space\(+\)\(38\)
Minus space\(-\)\(34\)

Trace form

\( 72 q + 648 q^{9} + O(q^{10}) \) \( 72 q + 648 q^{9} + 1800 q^{25} + 400 q^{29} + 464 q^{33} + 16 q^{37} + 80 q^{41} - 1968 q^{45} + 3528 q^{49} - 1568 q^{53} - 688 q^{57} + 1824 q^{61} + 2544 q^{69} - 5408 q^{77} + 6456 q^{81} - 2832 q^{85} + 1696 q^{89} + 4944 q^{93} + 2976 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(832))\) 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 13
832.4.a.a 832.a 1.a $1$ $49.090$ \(\Q\) None 13.4.a.a \(0\) \(-7\) \(7\) \(13\) $-$ $+$ $\mathrm{SU}(2)$ \(q-7q^{3}+7q^{5}+13q^{7}+22q^{9}-26q^{11}+\cdots\)
832.4.a.b 832.a 1.a $1$ $49.090$ \(\Q\) None 104.4.a.b \(0\) \(-5\) \(-19\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-5q^{3}-19q^{5}-3q^{7}-2q^{9}+2q^{11}+\cdots\)
832.4.a.c 832.a 1.a $1$ $49.090$ \(\Q\) None 416.4.a.a \(0\) \(-5\) \(3\) \(-5\) $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{3}+3q^{5}-5q^{7}-2q^{9}+30q^{11}+\cdots\)
832.4.a.d 832.a 1.a $1$ $49.090$ \(\Q\) None 26.4.a.c \(0\) \(-4\) \(18\) \(20\) $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{3}+18q^{5}+20q^{7}-11q^{9}+48q^{11}+\cdots\)
832.4.a.e 832.a 1.a $1$ $49.090$ \(\Q\) None 26.4.a.a \(0\) \(-3\) \(-11\) \(19\) $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-11q^{5}+19q^{7}-18q^{9}+38q^{11}+\cdots\)
832.4.a.f 832.a 1.a $1$ $49.090$ \(\Q\) None 52.4.a.a \(0\) \(-3\) \(13\) \(11\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+13q^{5}+11q^{7}-18q^{9}-2q^{11}+\cdots\)
832.4.a.g 832.a 1.a $1$ $49.090$ \(\Q\) None 26.4.a.b \(0\) \(-1\) \(-17\) \(35\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-17q^{5}+35q^{7}-26q^{9}+2q^{11}+\cdots\)
832.4.a.h 832.a 1.a $1$ $49.090$ \(\Q\) None 416.4.a.b \(0\) \(-1\) \(1\) \(5\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+5q^{7}-26q^{9}-10q^{11}+\cdots\)
832.4.a.i 832.a 1.a $1$ $49.090$ \(\Q\) None 104.4.a.a \(0\) \(-1\) \(7\) \(-21\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+7q^{5}-21q^{7}-26q^{9}-6q^{11}+\cdots\)
832.4.a.j 832.a 1.a $1$ $49.090$ \(\Q\) None 26.4.a.b \(0\) \(1\) \(-17\) \(-35\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-17q^{5}-35q^{7}-26q^{9}-2q^{11}+\cdots\)
832.4.a.k 832.a 1.a $1$ $49.090$ \(\Q\) None 416.4.a.b \(0\) \(1\) \(1\) \(-5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-5q^{7}-26q^{9}+10q^{11}+\cdots\)
832.4.a.l 832.a 1.a $1$ $49.090$ \(\Q\) None 104.4.a.a \(0\) \(1\) \(7\) \(21\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+7q^{5}+21q^{7}-26q^{9}+6q^{11}+\cdots\)
832.4.a.m 832.a 1.a $1$ $49.090$ \(\Q\) None 26.4.a.a \(0\) \(3\) \(-11\) \(-19\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-11q^{5}-19q^{7}-18q^{9}-38q^{11}+\cdots\)
832.4.a.n 832.a 1.a $1$ $49.090$ \(\Q\) None 52.4.a.a \(0\) \(3\) \(13\) \(-11\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+13q^{5}-11q^{7}-18q^{9}+2q^{11}+\cdots\)
832.4.a.o 832.a 1.a $1$ $49.090$ \(\Q\) None 26.4.a.c \(0\) \(4\) \(18\) \(-20\) $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{3}+18q^{5}-20q^{7}-11q^{9}-48q^{11}+\cdots\)
832.4.a.p 832.a 1.a $1$ $49.090$ \(\Q\) None 104.4.a.b \(0\) \(5\) \(-19\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+5q^{3}-19q^{5}+3q^{7}-2q^{9}-2q^{11}+\cdots\)
832.4.a.q 832.a 1.a $1$ $49.090$ \(\Q\) None 416.4.a.a \(0\) \(5\) \(3\) \(5\) $-$ $+$ $\mathrm{SU}(2)$ \(q+5q^{3}+3q^{5}+5q^{7}-2q^{9}-30q^{11}+\cdots\)
832.4.a.r 832.a 1.a $1$ $49.090$ \(\Q\) None 13.4.a.a \(0\) \(7\) \(7\) \(-13\) $+$ $+$ $\mathrm{SU}(2)$ \(q+7q^{3}+7q^{5}-13q^{7}+22q^{9}+26q^{11}+\cdots\)
832.4.a.s 832.a 1.a $2$ $49.090$ \(\Q(\sqrt{17}) \) None 13.4.a.b \(0\) \(-5\) \(3\) \(-9\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-3\beta )q^{3}+(1+\beta )q^{5}+(1-11\beta )q^{7}+\cdots\)
832.4.a.t 832.a 1.a $2$ $49.090$ \(\Q(\sqrt{217}) \) None 52.4.a.b \(0\) \(-3\) \(-23\) \(-27\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-11-\beta )q^{5}+(-13+\cdots)q^{7}+\cdots\)
832.4.a.u 832.a 1.a $2$ $49.090$ \(\Q(\sqrt{73}) \) None 104.4.a.c \(0\) \(-3\) \(3\) \(25\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(3-3\beta )q^{5}+(13-\beta )q^{7}+\cdots\)
832.4.a.v 832.a 1.a $2$ $49.090$ \(\Q(\sqrt{321}) \) None 104.4.a.d \(0\) \(-1\) \(11\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(6-\beta )q^{5}+(-2+3\beta )q^{7}+\cdots\)
832.4.a.w 832.a 1.a $2$ $49.090$ \(\Q(\sqrt{321}) \) None 104.4.a.d \(0\) \(1\) \(11\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(6-\beta )q^{5}+(2-3\beta )q^{7}+(53+\cdots)q^{9}+\cdots\)
832.4.a.x 832.a 1.a $2$ $49.090$ \(\Q(\sqrt{217}) \) None 52.4.a.b \(0\) \(3\) \(-23\) \(27\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-11-\beta )q^{5}+(13+\beta )q^{7}+\cdots\)
832.4.a.y 832.a 1.a $2$ $49.090$ \(\Q(\sqrt{73}) \) None 104.4.a.c \(0\) \(3\) \(3\) \(-25\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(3-3\beta )q^{5}+(-13+\beta )q^{7}+\cdots\)
832.4.a.z 832.a 1.a $2$ $49.090$ \(\Q(\sqrt{17}) \) None 13.4.a.b \(0\) \(5\) \(3\) \(9\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+3\beta )q^{3}+(1+\beta )q^{5}+(-1+11\beta )q^{7}+\cdots\)
832.4.a.ba 832.a 1.a $3$ $49.090$ 3.3.24965.1 None 416.4.a.e \(0\) \(-4\) \(-16\) \(-26\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-6-\beta _{1}+\beta _{2})q^{5}+\cdots\)
832.4.a.bb 832.a 1.a $3$ $49.090$ 3.3.18257.1 None 104.4.a.e \(0\) \(0\) \(8\) \(-36\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(3+2\beta _{1}+\beta _{2})q^{5}+(-12+\cdots)q^{7}+\cdots\)
832.4.a.bc 832.a 1.a $3$ $49.090$ 3.3.18257.1 None 104.4.a.e \(0\) \(0\) \(8\) \(36\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(3+2\beta _{1}+\beta _{2})q^{5}+(12+\beta _{1}+\cdots)q^{7}+\cdots\)
832.4.a.bd 832.a 1.a $3$ $49.090$ 3.3.24965.1 None 416.4.a.e \(0\) \(4\) \(-16\) \(26\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(-6-\beta _{1}+\beta _{2})q^{5}+\cdots\)
832.4.a.be 832.a 1.a $4$ $49.090$ 4.4.1847677.1 None 416.4.a.g \(0\) \(0\) \(14\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(3-\beta _{2})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
832.4.a.bf 832.a 1.a $5$ $49.090$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 416.4.a.h \(0\) \(-11\) \(5\) \(21\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(4+\beta _{1}+\cdots)q^{7}+\cdots\)
832.4.a.bg 832.a 1.a $5$ $49.090$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 416.4.a.h \(0\) \(11\) \(5\) \(-21\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(-4-\beta _{1}+\cdots)q^{7}+\cdots\)
832.4.a.bh 832.a 1.a $6$ $49.090$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 416.4.a.k \(0\) \(0\) \(-16\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-3+\beta _{5})q^{5}+(-2\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
832.4.a.bi 832.a 1.a $6$ $49.090$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 416.4.a.j \(0\) \(0\) \(16\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(3+\beta _{1})q^{5}-\beta _{4}q^{7}+(20+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(832))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(832)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 2}\)