Properties

Label 6272.2.a
Level $6272$
Weight $2$
Character orbit 6272.a
Rep. character $\chi_{6272}(1,\cdot)$
Character field $\Q$
Dimension $164$
Newform subspaces $52$
Sturm bound $1792$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 6272 = 2^{7} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6272.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 52 \)
Sturm bound: \(1792\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\), \(13\), \(23\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6272))\).

Total New Old
Modular forms 960 164 796
Cusp forms 833 164 669
Eisenstein series 127 0 127

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

\(2\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(36\)
\(+\)\(-\)\(-\)\(45\)
\(-\)\(+\)\(-\)\(44\)
\(-\)\(-\)\(+\)\(39\)
Plus space\(+\)\(75\)
Minus space\(-\)\(89\)

Trace form

\( 164 q + 164 q^{9} + O(q^{10}) \) \( 164 q + 164 q^{9} - 8 q^{17} + 156 q^{25} - 16 q^{33} - 24 q^{41} - 48 q^{57} + 16 q^{65} - 8 q^{73} + 180 q^{81} + 56 q^{89} - 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6272))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7
6272.2.a.a 6272.a 1.a $1$ $50.082$ \(\Q\) None \(0\) \(-2\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\)
6272.2.a.b 6272.a 1.a $1$ $50.082$ \(\Q\) None \(0\) \(-2\) \(2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots\)
6272.2.a.c 6272.a 1.a $1$ $50.082$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{9}-2q^{11}-4q^{13}+2q^{17}+4q^{19}+\cdots\)
6272.2.a.d 6272.a 1.a $1$ $50.082$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{9}-2q^{11}+4q^{13}+2q^{17}+4q^{19}+\cdots\)
6272.2.a.e 6272.a 1.a $1$ $50.082$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{9}+2q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots\)
6272.2.a.f 6272.a 1.a $1$ $50.082$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{9}+2q^{11}+4q^{13}+2q^{17}-4q^{19}+\cdots\)
6272.2.a.g 6272.a 1.a $1$ $50.082$ \(\Q\) None \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
6272.2.a.h 6272.a 1.a $1$ $50.082$ \(\Q\) None \(0\) \(2\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6272.2.a.i 6272.a 1.a $2$ $50.082$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(-1-\beta )q^{5}+(1-2\beta )q^{9}+\cdots\)
6272.2.a.j 6272.a 1.a $2$ $50.082$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(1+\beta )q^{5}+(1-2\beta )q^{9}+\cdots\)
6272.2.a.k 6272.a 1.a $2$ $50.082$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2\beta q^{5}-q^{9}-4q^{11}-4q^{15}+\cdots\)
6272.2.a.l 6272.a 1.a $2$ $50.082$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2\beta q^{5}-q^{9}-4q^{11}+4q^{15}+\cdots\)
6272.2.a.m 6272.a 1.a $2$ $50.082$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-\beta q^{5}-q^{9}+3\beta q^{13}-2q^{15}+\cdots\)
6272.2.a.n 6272.a 1.a $2$ $50.082$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-\beta q^{5}-q^{9}+3\beta q^{13}-2q^{15}+\cdots\)
6272.2.a.o 6272.a 1.a $2$ $50.082$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{5}-q^{9}-3\beta q^{13}+2q^{15}+\cdots\)
6272.2.a.p 6272.a 1.a $2$ $50.082$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{5}-q^{9}-3\beta q^{13}+2q^{15}+\cdots\)
6272.2.a.q 6272.a 1.a $2$ $50.082$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2\beta q^{5}-q^{9}+4q^{11}-4q^{15}+\cdots\)
6272.2.a.r 6272.a 1.a $2$ $50.082$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2\beta q^{5}-q^{9}+4q^{11}+4q^{15}+\cdots\)
6272.2.a.s 6272.a 1.a $2$ $50.082$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+(1+2\beta )q^{9}+\cdots\)
6272.2.a.t 6272.a 1.a $2$ $50.082$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1-\beta )q^{5}+(1+2\beta )q^{9}+\cdots\)
6272.2.a.u 6272.a 1.a $3$ $50.082$ 3.3.316.1 None \(0\) \(-2\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3+\cdots)q^{9}+\cdots\)
6272.2.a.v 6272.a 1.a $3$ $50.082$ 3.3.316.1 None \(0\) \(-2\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6272.2.a.w 6272.a 1.a $3$ $50.082$ 3.3.316.1 None \(0\) \(2\) \(-2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6272.2.a.x 6272.a 1.a $3$ $50.082$ 3.3.316.1 None \(0\) \(2\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6272.2.a.y 6272.a 1.a $4$ $50.082$ 4.4.54864.1 None \(0\) \(-2\) \(-2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.z 6272.a 1.a $4$ $50.082$ 4.4.11344.1 None \(0\) \(-2\) \(-2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.ba 6272.a 1.a $4$ $50.082$ 4.4.11344.1 None \(0\) \(-2\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bb 6272.a 1.a $4$ $50.082$ 4.4.54864.1 None \(0\) \(-2\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bc 6272.a 1.a $4$ $50.082$ 4.4.54864.1 None \(0\) \(-2\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bd 6272.a 1.a $4$ $50.082$ 4.4.11344.1 None \(0\) \(-2\) \(2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.be 6272.a 1.a $4$ $50.082$ 4.4.11344.1 None \(0\) \(-2\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.bf 6272.a 1.a $4$ $50.082$ 4.4.54864.1 None \(0\) \(-2\) \(2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bg 6272.a 1.a $4$ $50.082$ \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{9}+\cdots\)
6272.2.a.bh 6272.a 1.a $4$ $50.082$ \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{9}+(-1+\cdots)q^{11}+\cdots\)
6272.2.a.bi 6272.a 1.a $4$ $50.082$ \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{9}+\cdots\)
6272.2.a.bj 6272.a 1.a $4$ $50.082$ \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{9}+(1+\cdots)q^{11}+\cdots\)
6272.2.a.bk 6272.a 1.a $4$ $50.082$ 4.4.9248.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
6272.2.a.bl 6272.a 1.a $4$ $50.082$ 4.4.9248.1 None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
6272.2.a.bm 6272.a 1.a $4$ $50.082$ 4.4.9248.1 None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(1+\beta _{3})q^{11}+\cdots\)
6272.2.a.bn 6272.a 1.a $4$ $50.082$ 4.4.9248.1 None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(1+\beta _{3})q^{11}+\cdots\)
6272.2.a.bo 6272.a 1.a $4$ $50.082$ 4.4.54864.1 None \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bp 6272.a 1.a $4$ $50.082$ 4.4.11344.1 None \(0\) \(2\) \(-2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bq 6272.a 1.a $4$ $50.082$ 4.4.11344.1 None \(0\) \(2\) \(-2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.br 6272.a 1.a $4$ $50.082$ 4.4.54864.1 None \(0\) \(2\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bs 6272.a 1.a $4$ $50.082$ 4.4.54864.1 None \(0\) \(2\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bt 6272.a 1.a $4$ $50.082$ 4.4.11344.1 None \(0\) \(2\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.bu 6272.a 1.a $4$ $50.082$ 4.4.11344.1 None \(0\) \(2\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.bv 6272.a 1.a $4$ $50.082$ 4.4.54864.1 None \(0\) \(2\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bw 6272.a 1.a $6$ $50.082$ 6.6.26849792.2 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{4}+\cdots)q^{9}+\cdots\)
6272.2.a.bx 6272.a 1.a $6$ $50.082$ 6.6.26849792.2 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2-\beta _{4})q^{9}+\cdots\)
6272.2.a.by 6272.a 1.a $6$ $50.082$ 6.6.26849792.2 None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{4}+\cdots)q^{9}+\cdots\)
6272.2.a.bz 6272.a 1.a $6$ $50.082$ 6.6.26849792.2 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2-\beta _{4})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6272))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6272)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(896))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1568))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3136))\)\(^{\oplus 2}\)