Properties

Label 7168.2.a
Level $7168$
Weight $2$
Character orbit 7168.a
Rep. character $\chi_{7168}(1,\cdot)$
Character field $\Q$
Dimension $192$
Newform subspaces $38$
Sturm bound $2048$
Trace bound $17$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 7168 = 2^{10} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7168.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 38 \)
Sturm bound: \(2048\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\), \(13\), \(17\), \(23\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7168))\).

Total New Old
Modular forms 1072 192 880
Cusp forms 977 192 785
Eisenstein series 95 0 95

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.
\(+\)\(+\)\(+\)\(48\)
\(+\)\(-\)\(-\)\(52\)
\(-\)\(+\)\(-\)\(48\)
\(-\)\(-\)\(+\)\(44\)
Plus space\(+\)\(92\)
Minus space\(-\)\(100\)

Trace form

\( 192q + 192q^{9} + O(q^{10}) \) \( 192q + 192q^{9} + 192q^{25} + 192q^{49} + 192q^{81} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7168))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
7168.2.a.a \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(q+\beta q^{5}-q^{7}-3q^{9}+4\beta q^{11}+3\beta q^{13}+\cdots\)
7168.2.a.b \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(q+2\beta q^{5}-q^{7}-3q^{9}-\beta q^{11}+2q^{17}+\cdots\)
7168.2.a.c \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(q+\beta q^{3}-2\beta q^{5}-q^{7}-q^{9}-2\beta q^{11}+\cdots\)
7168.2.a.d \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(q+\beta q^{3}-2\beta q^{5}-q^{7}-q^{9}+2\beta q^{11}+\cdots\)
7168.2.a.e \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(q+\beta q^{3}-q^{7}-q^{9}-2\beta q^{11}+2\beta q^{13}+\cdots\)
7168.2.a.f \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(q+\beta q^{3}+2\beta q^{5}-q^{7}-q^{9}+4\beta q^{11}+\cdots\)
7168.2.a.g \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(q+\beta q^{3}+2\beta q^{5}-q^{7}-q^{9}-2\beta q^{11}+\cdots\)
7168.2.a.h \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(q+2\beta q^{3}+\beta q^{5}-q^{7}+5q^{9}-4\beta q^{11}+\cdots\)
7168.2.a.i \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(q+2\beta q^{3}+2\beta q^{5}-q^{7}+5q^{9}+3\beta q^{11}+\cdots\)
7168.2.a.j \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(q-\beta q^{5}+q^{7}-3q^{9}+4\beta q^{11}-3\beta q^{13}+\cdots\)
7168.2.a.k \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(q+2\beta q^{5}+q^{7}-3q^{9}+\beta q^{11}+2q^{17}+\cdots\)
7168.2.a.l \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(q+\beta q^{3}-2\beta q^{5}+q^{7}-q^{9}+4\beta q^{11}+\cdots\)
7168.2.a.m \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(q+\beta q^{3}-2\beta q^{5}+q^{7}-q^{9}-2\beta q^{11}+\cdots\)
7168.2.a.n \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(q+\beta q^{3}+q^{7}-q^{9}-2\beta q^{11}-2\beta q^{13}+\cdots\)
7168.2.a.o \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(q+\beta q^{3}+2\beta q^{5}+q^{7}-q^{9}-2\beta q^{11}+\cdots\)
7168.2.a.p \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(q+\beta q^{3}+2\beta q^{5}+q^{7}-q^{9}+2\beta q^{11}+\cdots\)
7168.2.a.q \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(q+2\beta q^{3}-2\beta q^{5}+q^{7}+5q^{9}+3\beta q^{11}+\cdots\)
7168.2.a.r \(2\) \(57.237\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(q+2\beta q^{3}-\beta q^{5}+q^{7}+5q^{9}-4\beta q^{11}+\cdots\)
7168.2.a.s \(4\) \(57.237\) 4.4.4352.1 None \(0\) \(0\) \(-4\) \(-4\) \(+\) \(+\) \(q+(-\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
7168.2.a.t \(4\) \(57.237\) 4.4.4352.1 None \(0\) \(0\) \(-4\) \(4\) \(-\) \(-\) \(q+(\beta _{1}-\beta _{3})q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
7168.2.a.u \(4\) \(57.237\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}-q^{7}+3q^{9}+\cdots\)
7168.2.a.v \(4\) \(57.237\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(-\) \(q+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+q^{7}+3q^{9}+\cdots\)
7168.2.a.w \(4\) \(57.237\) 4.4.4352.1 None \(0\) \(0\) \(4\) \(-4\) \(-\) \(+\) \(q+(\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}-\beta _{3})q^{5}-q^{7}+\cdots\)
7168.2.a.x \(4\) \(57.237\) 4.4.4352.1 None \(0\) \(0\) \(4\) \(4\) \(+\) \(-\) \(q+(-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}-\beta _{3})q^{5}+\cdots\)
7168.2.a.y \(6\) \(57.237\) 6.6.12781568.1 None \(0\) \(0\) \(0\) \(-6\) \(+\) \(+\) \(q-\beta _{4}q^{3}+(\beta _{2}+\beta _{4})q^{5}-q^{7}+(3+\beta _{5})q^{9}+\cdots\)
7168.2.a.z \(6\) \(57.237\) 6.6.12781568.1 None \(0\) \(0\) \(0\) \(6\) \(+\) \(-\) \(q-\beta _{4}q^{3}+(-\beta _{2}-\beta _{4})q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
7168.2.a.ba \(8\) \(57.237\) 8.8.9433055232.1 None \(0\) \(0\) \(-8\) \(-8\) \(+\) \(+\) \(q-\beta _{5}q^{3}+(-1-\beta _{2})q^{5}-q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7168.2.a.bb \(8\) \(57.237\) 8.8.9433055232.1 None \(0\) \(0\) \(-8\) \(8\) \(-\) \(-\) \(q+\beta _{5}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7168.2.a.bc \(8\) \(57.237\) 8.8.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-8\) \(+\) \(+\) \(q-\beta _{7}q^{3}-\beta _{3}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
7168.2.a.bd \(8\) \(57.237\) 8.8.\(\cdots\).1 None \(0\) \(0\) \(0\) \(8\) \(-\) \(-\) \(q-\beta _{7}q^{3}+\beta _{3}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
7168.2.a.be \(8\) \(57.237\) 8.8.9433055232.1 None \(0\) \(0\) \(8\) \(-8\) \(-\) \(+\) \(q+\beta _{5}q^{3}+(1+\beta _{2})q^{5}-q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7168.2.a.bf \(8\) \(57.237\) 8.8.9433055232.1 None \(0\) \(0\) \(8\) \(8\) \(+\) \(-\) \(q-\beta _{5}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7168.2.a.bg \(12\) \(57.237\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-8\) \(0\) \(-12\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{3}+\beta _{5}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
7168.2.a.bh \(12\) \(57.237\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-8\) \(0\) \(12\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{3}-\beta _{5}q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
7168.2.a.bi \(12\) \(57.237\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-12\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{4})q^{5}-q^{7}+\cdots\)
7168.2.a.bj \(12\) \(57.237\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(12\) \(+\) \(-\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\beta _{4})q^{5}+q^{7}+\cdots\)
7168.2.a.bk \(12\) \(57.237\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(8\) \(0\) \(-12\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}-\beta _{5}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
7168.2.a.bl \(12\) \(57.237\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(8\) \(0\) \(12\) \(+\) \(-\) \(q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7168))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7168)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(512))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(896))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1024))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1792))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3584))\)\(^{\oplus 2}\)