Properties

Label 9248.2.a
Level $9248$
Weight $2$
Character orbit 9248.a
Rep. character $\chi_{9248}(1,\cdot)$
Character field $\Q$
Dimension $271$
Newform subspaces $52$
Sturm bound $2448$
Trace bound $145$

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Defining parameters

Level: \( N \) \(=\) \( 9248 = 2^{5} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9248.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 52 \)
Sturm bound: \(2448\)
Trace bound: \(145\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(19\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9248))\).

Total New Old
Modular forms 1296 271 1025
Cusp forms 1153 271 882
Eisenstein series 143 0 143

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

\(2\)\(17\)FrickeDim
\(+\)\(+\)\(+\)\(64\)
\(+\)\(-\)\(-\)\(72\)
\(-\)\(+\)\(-\)\(71\)
\(-\)\(-\)\(+\)\(64\)
Plus space\(+\)\(128\)
Minus space\(-\)\(143\)

Trace form

\( 271 q + 2 q^{5} + 275 q^{9} + 10 q^{13} + 257 q^{25} - 6 q^{29} - 16 q^{33} + 18 q^{37} - 26 q^{41} + 26 q^{45} + 263 q^{49} + 34 q^{53} - 16 q^{57} + 26 q^{61} - 36 q^{65} + 32 q^{69} + 6 q^{73} + 279 q^{81}+ \cdots + 30 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9248))\) 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 17
9248.2.a.a 9248.a 1.a $1$ $73.846$ \(\Q\) None 544.2.a.b \(0\) \(-2\) \(-4\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
9248.2.a.b 9248.a 1.a $1$ $73.846$ \(\Q\) None 544.2.a.a \(0\) \(-2\) \(-2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
9248.2.a.c 9248.a 1.a $1$ $73.846$ \(\Q\) \(\Q(\sqrt{-1}) \) 544.2.b.a \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-4q^{5}-3q^{9}-6q^{13}+11q^{25}-4q^{29}+\cdots\)
9248.2.a.d 9248.a 1.a $1$ $73.846$ \(\Q\) None 544.2.a.c \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}-4q^{11}+2q^{13}+4q^{19}+\cdots\)
9248.2.a.e 9248.a 1.a $1$ $73.846$ \(\Q\) None 544.2.a.c \(0\) \(0\) \(0\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}+4q^{11}+2q^{13}-4q^{19}+\cdots\)
9248.2.a.f 9248.a 1.a $1$ $73.846$ \(\Q\) \(\Q(\sqrt{-1}) \) 32.2.a.a \(0\) \(0\) \(2\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+2q^{5}-3q^{9}+6q^{13}-q^{25}+10q^{29}+\cdots\)
9248.2.a.g 9248.a 1.a $1$ $73.846$ \(\Q\) \(\Q(\sqrt{-1}) \) 544.2.b.a \(0\) \(0\) \(4\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+4q^{5}-3q^{9}-6q^{13}+11q^{25}+4q^{29}+\cdots\)
9248.2.a.h 9248.a 1.a $1$ $73.846$ \(\Q\) None 544.2.a.b \(0\) \(2\) \(-4\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
9248.2.a.i 9248.a 1.a $1$ $73.846$ \(\Q\) None 544.2.a.a \(0\) \(2\) \(-2\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
9248.2.a.j 9248.a 1.a $2$ $73.846$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) 544.2.o.d \(0\) \(0\) \(0\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-3\beta q^{5}-3q^{9}-4q^{13}+13q^{25}+\cdots\)
9248.2.a.k 9248.a 1.a $2$ $73.846$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) 544.2.o.c \(0\) \(0\) \(0\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-\beta q^{5}-3q^{9}+4q^{13}-3q^{25}-3\beta q^{29}+\cdots\)
9248.2.a.l 9248.a 1.a $2$ $73.846$ \(\Q(\sqrt{2}) \) None 544.2.o.b \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2\beta q^{5}-q^{9}+3\beta q^{11}+2q^{13}+\cdots\)
9248.2.a.m 9248.a 1.a $2$ $73.846$ \(\Q(\sqrt{2}) \) None 544.2.o.b \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2\beta q^{5}-q^{9}+3\beta q^{11}+2q^{13}+\cdots\)
9248.2.a.n 9248.a 1.a $2$ $73.846$ \(\Q(\sqrt{2}) \) None 544.2.o.a \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}-\beta q^{5}-2\beta q^{7}+5q^{9}+2\beta q^{11}+\cdots\)
9248.2.a.o 9248.a 1.a $2$ $73.846$ \(\Q(\sqrt{2}) \) None 544.2.o.a \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}+\beta q^{5}-2\beta q^{7}+5q^{9}+2\beta q^{11}+\cdots\)
9248.2.a.p 9248.a 1.a $2$ $73.846$ \(\Q(\sqrt{2}) \) None 544.2.a.g \(0\) \(0\) \(4\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2q^{5}-3\beta q^{7}-q^{9}+\beta q^{11}+\cdots\)
9248.2.a.q 9248.a 1.a $2$ $73.846$ \(\Q(\sqrt{10}) \) None 544.2.a.h \(0\) \(0\) \(4\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2q^{5}+\beta q^{7}+7q^{9}+\beta q^{11}+\cdots\)
9248.2.a.r 9248.a 1.a $3$ $73.846$ \(\Q(\zeta_{18})^+\) None 9248.2.a.r \(0\) \(-3\) \(0\) \(9\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(3+\cdots)q^{7}+\cdots\)
9248.2.a.s 9248.a 1.a $3$ $73.846$ \(\Q(\zeta_{18})^+\) None 9248.2.a.r \(0\) \(-3\) \(0\) \(9\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
9248.2.a.t 9248.a 1.a $3$ $73.846$ 3.3.148.1 None 544.2.a.i \(0\) \(-2\) \(2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
9248.2.a.u 9248.a 1.a $3$ $73.846$ 3.3.148.1 None 544.2.a.i \(0\) \(2\) \(2\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1-\beta _{2})q^{7}+\cdots\)
9248.2.a.v 9248.a 1.a $3$ $73.846$ \(\Q(\zeta_{18})^+\) None 9248.2.a.r \(0\) \(3\) \(0\) \(-9\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-3+\beta _{1}+\cdots)q^{7}+\cdots\)
9248.2.a.w 9248.a 1.a $3$ $73.846$ \(\Q(\zeta_{18})^+\) None 9248.2.a.r \(0\) \(3\) \(0\) \(-9\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-3+\cdots)q^{7}+\cdots\)
9248.2.a.x 9248.a 1.a $4$ $73.846$ 4.4.14272.1 None 9248.2.a.x \(0\) \(-2\) \(-2\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
9248.2.a.y 9248.a 1.a $4$ $73.846$ 4.4.14272.1 None 9248.2.a.x \(0\) \(-2\) \(2\) \(-6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
9248.2.a.z 9248.a 1.a $4$ $73.846$ 4.4.45968.1 None 9248.2.a.z \(0\) \(0\) \(-6\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}-\beta _{3}q^{7}+(2+\cdots)q^{9}+\cdots\)
9248.2.a.ba 9248.a 1.a $4$ $73.846$ \(\Q(\sqrt{3}, \sqrt{7})\) None 9248.2.a.ba \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+\beta _{2}q^{5}-\beta _{1}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
9248.2.a.bb 9248.a 1.a $4$ $73.846$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-1}) \) 544.2.bb.b \(0\) \(0\) \(0\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+(\beta _{1}+2\beta _{3})q^{5}-3q^{9}-\beta _{2}q^{13}+(5+\cdots)q^{25}+\cdots\)
9248.2.a.bc 9248.a 1.a $4$ $73.846$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-1}) \) 544.2.bb.a \(0\) \(0\) \(0\) \(0\) $+$ $-$ $N(\mathrm{U}(1))$ \(q+(2\beta _{1}+\beta _{3})q^{5}-3q^{9}+5\beta _{2}q^{13}+\cdots\)
9248.2.a.bd 9248.a 1.a $4$ $73.846$ \(\Q(\zeta_{16})^+\) None 544.2.b.d \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+\cdots\)
9248.2.a.be 9248.a 1.a $4$ $73.846$ \(\Q(\zeta_{16})^+\) None 544.2.b.d \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
9248.2.a.bf 9248.a 1.a $4$ $73.846$ 4.4.9248.1 \(\Q(\sqrt{-17}) \) 544.2.b.c \(0\) \(0\) \(0\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q+\beta _{1}q^{3}+\beta _{1}q^{7}+(2-\beta _{3})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
9248.2.a.bg 9248.a 1.a $4$ $73.846$ 4.4.9248.1 \(\Q(\sqrt{-17}) \) 544.2.b.b \(0\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{7}+(4+\beta _{3})q^{9}+\cdots\)
9248.2.a.bh 9248.a 1.a $4$ $73.846$ \(\Q(\sqrt{3}, \sqrt{7})\) None 9248.2.a.ba \(0\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
9248.2.a.bi 9248.a 1.a $4$ $73.846$ 4.4.45968.1 None 9248.2.a.z \(0\) \(0\) \(6\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}-\beta _{3}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
9248.2.a.bj 9248.a 1.a $4$ $73.846$ 4.4.14272.1 None 9248.2.a.x \(0\) \(2\) \(-2\) \(6\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
9248.2.a.bk 9248.a 1.a $4$ $73.846$ 4.4.14272.1 None 9248.2.a.x \(0\) \(2\) \(2\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
9248.2.a.bl 9248.a 1.a $6$ $73.846$ 6.6.3359232.1 None 544.2.o.g \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{5}q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
9248.2.a.bm 9248.a 1.a $6$ $73.846$ 6.6.3359232.1 None 544.2.o.g \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{5}q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
9248.2.a.bn 9248.a 1.a $8$ $73.846$ 8.8.3288334336.1 None 544.2.bb.c \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots\)
9248.2.a.bo 9248.a 1.a $9$ $73.846$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 9248.2.a.bo \(0\) \(-9\) \(-6\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
9248.2.a.bp 9248.a 1.a $9$ $73.846$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 9248.2.a.bo \(0\) \(-9\) \(6\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)
9248.2.a.bq 9248.a 1.a $9$ $73.846$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 9248.2.a.bo \(0\) \(9\) \(-6\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
9248.2.a.br 9248.a 1.a $9$ $73.846$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 9248.2.a.bo \(0\) \(9\) \(6\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{5}+\beta _{6})q^{5}+\cdots\)
9248.2.a.bs 9248.a 1.a $12$ $73.846$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 9248.2.a.bs \(0\) \(0\) \(-12\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{2}+\beta _{5})q^{5}+\beta _{8}q^{7}+\cdots\)
9248.2.a.bt 9248.a 1.a $12$ $73.846$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 9248.2.a.bt \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}-\beta _{11})q^{7}+\cdots\)
9248.2.a.bu 9248.a 1.a $12$ $73.846$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 9248.2.a.bt \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{1}-\beta _{11})q^{7}+\cdots\)
9248.2.a.bv 9248.a 1.a $12$ $73.846$ 12.12.\(\cdots\).1 None 544.2.o.i \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{6}q^{3}-\beta _{4}q^{5}+(-\beta _{6}+\beta _{11})q^{7}+\cdots\)
9248.2.a.bw 9248.a 1.a $12$ $73.846$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 9248.2.a.bs \(0\) \(0\) \(12\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{2}-\beta _{5})q^{5}+\beta _{8}q^{7}+\cdots\)
9248.2.a.bx 9248.a 1.a $16$ $73.846$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 544.2.bb.d \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{6}-\beta _{12})q^{5}+(\beta _{1}-\beta _{9}+\cdots)q^{7}+\cdots\)
9248.2.a.by 9248.a 1.a $20$ $73.846$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 544.2.bb.e \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{17}q^{3}-\beta _{5}q^{5}-\beta _{12}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
9248.2.a.bz 9248.a 1.a $20$ $73.846$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 544.2.bb.e \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{17}q^{3}+\beta _{5}q^{5}-\beta _{12}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9248))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9248)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(544))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2312))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4624))\)\(^{\oplus 2}\)