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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
6272.2.a.a \(1\) \(50.082\) \(\Q\) None \(0\) \(-2\) \(-2\) \(0\) \(-\) \(-\) \(q-2q^{3}-2q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\)
6272.2.a.b \(1\) \(50.082\) \(\Q\) None \(0\) \(-2\) \(2\) \(0\) \(-\) \(-\) \(q-2q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots\)
6272.2.a.c \(1\) \(50.082\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q-3q^{9}-2q^{11}-4q^{13}+2q^{17}+4q^{19}+\cdots\)
6272.2.a.d \(1\) \(50.082\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q-3q^{9}-2q^{11}+4q^{13}+2q^{17}+4q^{19}+\cdots\)
6272.2.a.e \(1\) \(50.082\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q-3q^{9}+2q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots\)
6272.2.a.f \(1\) \(50.082\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q-3q^{9}+2q^{11}+4q^{13}+2q^{17}-4q^{19}+\cdots\)
6272.2.a.g \(1\) \(50.082\) \(\Q\) None \(0\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(q+2q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
6272.2.a.h \(1\) \(50.082\) \(\Q\) None \(0\) \(2\) \(2\) \(0\) \(+\) \(-\) \(q+2q^{3}+2q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6272.2.a.i \(2\) \(50.082\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(-\) \(q+(-1+\beta )q^{3}+(-1-\beta )q^{5}+(1-2\beta )q^{9}+\cdots\)
6272.2.a.j \(2\) \(50.082\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(0\) \(-\) \(-\) \(q+(-1+\beta )q^{3}+(1+\beta )q^{5}+(1-2\beta )q^{9}+\cdots\)
6272.2.a.k \(2\) \(50.082\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta q^{3}-2\beta q^{5}-q^{9}-4q^{11}-4q^{15}+\cdots\)
6272.2.a.l \(2\) \(50.082\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+\beta q^{3}+2\beta q^{5}-q^{9}-4q^{11}+4q^{15}+\cdots\)
6272.2.a.m \(2\) \(50.082\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q+\beta q^{3}-\beta q^{5}-q^{9}+3\beta q^{13}-2q^{15}+\cdots\)
6272.2.a.n \(2\) \(50.082\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+\beta q^{3}-\beta q^{5}-q^{9}+3\beta q^{13}-2q^{15}+\cdots\)
6272.2.a.o \(2\) \(50.082\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+\beta q^{3}+\beta q^{5}-q^{9}-3\beta q^{13}+2q^{15}+\cdots\)
6272.2.a.p \(2\) \(50.082\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+\beta q^{3}+\beta q^{5}-q^{9}-3\beta q^{13}+2q^{15}+\cdots\)
6272.2.a.q \(2\) \(50.082\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta q^{3}-2\beta q^{5}-q^{9}+4q^{11}-4q^{15}+\cdots\)
6272.2.a.r \(2\) \(50.082\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta q^{3}+2\beta q^{5}-q^{9}+4q^{11}+4q^{15}+\cdots\)
6272.2.a.s \(2\) \(50.082\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+(1+2\beta )q^{9}+\cdots\)
6272.2.a.t \(2\) \(50.082\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(0\) \(-\) \(-\) \(q+(1+\beta )q^{3}+(1-\beta )q^{5}+(1+2\beta )q^{9}+\cdots\)
6272.2.a.u \(3\) \(50.082\) 3.3.316.1 None \(0\) \(-2\) \(-2\) \(0\) \(-\) \(-\) \(q+(-1-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3+\cdots)q^{9}+\cdots\)
6272.2.a.v \(3\) \(50.082\) 3.3.316.1 None \(0\) \(-2\) \(2\) \(0\) \(+\) \(-\) \(q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6272.2.a.w \(3\) \(50.082\) 3.3.316.1 None \(0\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6272.2.a.x \(3\) \(50.082\) 3.3.316.1 None \(0\) \(2\) \(2\) \(0\) \(+\) \(-\) \(q+(1+\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6272.2.a.y \(4\) \(50.082\) 4.4.54864.1 None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.z \(4\) \(50.082\) 4.4.11344.1 None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(q+\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.ba \(4\) \(50.082\) 4.4.11344.1 None \(0\) \(-2\) \(-2\) \(0\) \(-\) \(-\) \(q+\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bb \(4\) \(50.082\) 4.4.54864.1 None \(0\) \(-2\) \(-2\) \(0\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bc \(4\) \(50.082\) 4.4.54864.1 None \(0\) \(-2\) \(2\) \(0\) \(-\) \(+\) \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bd \(4\) \(50.082\) 4.4.11344.1 None \(0\) \(-2\) \(2\) \(0\) \(+\) \(+\) \(q+\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.be \(4\) \(50.082\) 4.4.11344.1 None \(0\) \(-2\) \(2\) \(0\) \(+\) \(-\) \(q+\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.bf \(4\) \(50.082\) 4.4.54864.1 None \(0\) \(-2\) \(2\) \(0\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bg \(4\) \(50.082\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{9}+\cdots\)
6272.2.a.bh \(4\) \(50.082\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{9}+(-1+\cdots)q^{11}+\cdots\)
6272.2.a.bi \(4\) \(50.082\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{9}+\cdots\)
6272.2.a.bj \(4\) \(50.082\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{9}+(1+\cdots)q^{11}+\cdots\)
6272.2.a.bk \(4\) \(50.082\) 4.4.9248.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
6272.2.a.bl \(4\) \(50.082\) 4.4.9248.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
6272.2.a.bm \(4\) \(50.082\) 4.4.9248.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(1+\beta _{3})q^{11}+\cdots\)
6272.2.a.bn \(4\) \(50.082\) 4.4.9248.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(1+\beta _{3})q^{11}+\cdots\)
6272.2.a.bo \(4\) \(50.082\) 4.4.54864.1 None \(0\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bp \(4\) \(50.082\) 4.4.11344.1 None \(0\) \(2\) \(-2\) \(0\) \(+\) \(+\) \(q-\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bq \(4\) \(50.082\) 4.4.11344.1 None \(0\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(q-\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.br \(4\) \(50.082\) 4.4.54864.1 None \(0\) \(2\) \(-2\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bs \(4\) \(50.082\) 4.4.54864.1 None \(0\) \(2\) \(2\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bt \(4\) \(50.082\) 4.4.11344.1 None \(0\) \(2\) \(2\) \(0\) \(-\) \(+\) \(q-\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.bu \(4\) \(50.082\) 4.4.11344.1 None \(0\) \(2\) \(2\) \(0\) \(+\) \(-\) \(q-\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.bv \(4\) \(50.082\) 4.4.54864.1 None \(0\) \(2\) \(2\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bw \(6\) \(50.082\) 6.6.26849792.2 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{4}+\cdots)q^{9}+\cdots\)
6272.2.a.bx \(6\) \(50.082\) 6.6.26849792.2 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2-\beta _{4})q^{9}+\cdots\)
6272.2.a.by \(6\) \(50.082\) 6.6.26849792.2 None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{4}+\cdots)q^{9}+\cdots\)
6272.2.a.bz \(6\) \(50.082\) 6.6.26849792.2 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2-\beta _{4})q^{9}+\cdots\)

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

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