Properties

Label 867.4.a
Level $867$
Weight $4$
Character orbit 867.a
Rep. character $\chi_{867}(1,\cdot)$
Character field $\Q$
Dimension $136$
Newform subspaces $23$
Sturm bound $408$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 867 = 3 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 867.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(408\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(867))\).

Total New Old
Modular forms 324 136 188
Cusp forms 288 136 152
Eisenstein series 36 0 36

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

\(3\)\(17\)FrickeDim
\(+\)\(+\)\(+\)\(35\)
\(+\)\(-\)\(-\)\(33\)
\(-\)\(+\)\(-\)\(29\)
\(-\)\(-\)\(+\)\(39\)
Plus space\(+\)\(74\)
Minus space\(-\)\(62\)

Trace form

\( 136 q - 4 q^{2} + 564 q^{4} - 12 q^{6} - 8 q^{7} - 48 q^{8} + 1224 q^{9} - 100 q^{10} - 16 q^{11} - 28 q^{13} + 288 q^{14} + 84 q^{15} + 2348 q^{16} - 36 q^{18} + 192 q^{19} - 32 q^{20} + 84 q^{21} + 284 q^{22}+ \cdots - 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(867))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 17
867.4.a.a 867.a 1.a $1$ $51.155$ \(\Q\) None 867.4.a.a \(-3\) \(-3\) \(9\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{2}-3q^{3}+q^{4}+9q^{5}+9q^{6}+\cdots\)
867.4.a.b 867.a 1.a $1$ $51.155$ \(\Q\) None 867.4.a.a \(-3\) \(3\) \(-9\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{2}+3q^{3}+q^{4}-9q^{5}-9q^{6}+\cdots\)
867.4.a.c 867.a 1.a $1$ $51.155$ \(\Q\) None 51.4.a.b \(-1\) \(-3\) \(20\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}-7q^{4}+20q^{5}+3q^{6}+\cdots\)
867.4.a.d 867.a 1.a $1$ $51.155$ \(\Q\) None 51.4.a.a \(-1\) \(3\) \(-16\) \(-34\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}-7q^{4}-2^{4}q^{5}-3q^{6}+\cdots\)
867.4.a.e 867.a 1.a $1$ $51.155$ \(\Q\) None 51.4.a.c \(1\) \(3\) \(10\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}-7q^{4}+10q^{5}+3q^{6}+\cdots\)
867.4.a.f 867.a 1.a $1$ $51.155$ \(\Q\) None 867.4.a.f \(4\) \(-3\) \(2\) \(31\) $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-3q^{3}+8q^{4}+2q^{5}-12q^{6}+\cdots\)
867.4.a.g 867.a 1.a $1$ $51.155$ \(\Q\) None 867.4.a.f \(4\) \(3\) \(-2\) \(-31\) $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+3q^{3}+8q^{4}-2q^{5}+12q^{6}+\cdots\)
867.4.a.h 867.a 1.a $2$ $51.155$ \(\Q(\sqrt{13}) \) None 867.4.a.h \(-4\) \(-6\) \(-20\) \(-6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{2}-3q^{3}+(9+4\beta )q^{4}+\cdots\)
867.4.a.i 867.a 1.a $2$ $51.155$ \(\Q(\sqrt{13}) \) None 867.4.a.h \(-4\) \(6\) \(20\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{2}+3q^{3}+(9+4\beta )q^{4}+\cdots\)
867.4.a.j 867.a 1.a $2$ $51.155$ \(\Q(\sqrt{2}) \) None 51.4.a.d \(0\) \(6\) \(-6\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3q^{3}+10q^{4}+(-3-4\beta )q^{5}+\cdots\)
867.4.a.k 867.a 1.a $3$ $51.155$ 3.3.5912.1 None 51.4.a.e \(5\) \(-9\) \(-8\) \(8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}-3q^{3}+(5-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
867.4.a.l 867.a 1.a $4$ $51.155$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 867.4.a.l \(1\) \(-12\) \(-9\) \(-35\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2})q^{4}+\cdots\)
867.4.a.m 867.a 1.a $4$ $51.155$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 867.4.a.l \(1\) \(12\) \(9\) \(35\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(4-\beta _{1}+\beta _{2})q^{4}+\cdots\)
867.4.a.n 867.a 1.a $4$ $51.155$ 4.4.2873868.1 None 51.4.d.a \(2\) \(-12\) \(12\) \(14\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
867.4.a.o 867.a 1.a $4$ $51.155$ 4.4.2873868.1 None 51.4.d.a \(2\) \(12\) \(-12\) \(-14\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
867.4.a.p 867.a 1.a $8$ $51.155$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 51.4.e.a \(-4\) \(-24\) \(24\) \(28\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
867.4.a.q 867.a 1.a $8$ $51.155$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 51.4.e.a \(-4\) \(24\) \(-24\) \(-28\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+3q^{3}+(4-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
867.4.a.r 867.a 1.a $9$ $51.155$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 867.4.a.r \(-6\) \(-27\) \(-6\) \(33\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-3q^{3}+(2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
867.4.a.s 867.a 1.a $9$ $51.155$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 867.4.a.r \(-6\) \(27\) \(6\) \(-33\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+3q^{3}+(2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
867.4.a.t 867.a 1.a $15$ $51.155$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 867.4.a.t \(6\) \(-45\) \(-6\) \(-33\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
867.4.a.u 867.a 1.a $15$ $51.155$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 867.4.a.t \(6\) \(45\) \(6\) \(33\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
867.4.a.v 867.a 1.a $20$ $51.155$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 51.4.h.a \(0\) \(-60\) \(-32\) \(-56\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
867.4.a.w 867.a 1.a $20$ $51.155$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 51.4.h.a \(0\) \(60\) \(32\) \(56\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}+(2-\beta _{16}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(867))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(867)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 2}\)