Properties

Label 1792.2.a
Level $1792$
Weight $2$
Character orbit 1792.a
Rep. character $\chi_{1792}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $24$
Sturm bound $512$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(512\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(5\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1792))\).

Total New Old
Modular forms 280 48 232
Cusp forms 233 48 185
Eisenstein series 47 0 47

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.
\(+\)\(+\)\(+\)\(12\)
\(+\)\(-\)\(-\)\(14\)
\(-\)\(+\)\(-\)\(12\)
\(-\)\(-\)\(+\)\(10\)
Plus space\(+\)\(22\)
Minus space\(-\)\(26\)

Trace form

\( 48q + 48q^{9} + O(q^{10}) \) \( 48q + 48q^{9} + 48q^{25} + 48q^{49} - 32q^{65} - 32q^{73} + 48q^{81} - 32q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1792))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
1792.2.a.a \(1\) \(14.309\) \(\Q\) None \(0\) \(-2\) \(-4\) \(1\) \(-\) \(-\) \(q-2q^{3}-4q^{5}+q^{7}+q^{9}-2q^{11}+\cdots\)
1792.2.a.b \(1\) \(14.309\) \(\Q\) None \(0\) \(-2\) \(-2\) \(1\) \(-\) \(-\) \(q-2q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}+\cdots\)
1792.2.a.c \(1\) \(14.309\) \(\Q\) None \(0\) \(-2\) \(2\) \(-1\) \(+\) \(+\) \(q-2q^{3}+2q^{5}-q^{7}+q^{9}-2q^{13}+\cdots\)
1792.2.a.d \(1\) \(14.309\) \(\Q\) None \(0\) \(-2\) \(4\) \(-1\) \(-\) \(+\) \(q-2q^{3}+4q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
1792.2.a.e \(1\) \(14.309\) \(\Q\) None \(0\) \(2\) \(-4\) \(-1\) \(+\) \(+\) \(q+2q^{3}-4q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
1792.2.a.f \(1\) \(14.309\) \(\Q\) None \(0\) \(2\) \(-2\) \(-1\) \(-\) \(+\) \(q+2q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+\cdots\)
1792.2.a.g \(1\) \(14.309\) \(\Q\) None \(0\) \(2\) \(2\) \(1\) \(+\) \(-\) \(q+2q^{3}+2q^{5}+q^{7}+q^{9}-2q^{13}+\cdots\)
1792.2.a.h \(1\) \(14.309\) \(\Q\) None \(0\) \(2\) \(4\) \(1\) \(+\) \(-\) \(q+2q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+\cdots\)
1792.2.a.i \(2\) \(14.309\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(q+(-1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+\cdots\)
1792.2.a.j \(2\) \(14.309\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(q+(-1-\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+\cdots\)
1792.2.a.k \(2\) \(14.309\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(2\) \(+\) \(-\) \(q+(-1+\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
1792.2.a.l \(2\) \(14.309\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(2\) \(-\) \(-\) \(q+(-1-\beta )q^{3}+(1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
1792.2.a.m \(2\) \(14.309\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(q+\beta q^{5}-q^{7}-3q^{9}+\beta q^{11}-\beta q^{13}+\cdots\)
1792.2.a.n \(2\) \(14.309\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(q+\beta q^{3}+\beta q^{5}-q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1792.2.a.o \(2\) \(14.309\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(q-\beta q^{5}+q^{7}-3q^{9}+\beta q^{11}+\beta q^{13}+\cdots\)
1792.2.a.p \(2\) \(14.309\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(q+\beta q^{3}-\beta q^{5}+q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1792.2.a.q \(2\) \(14.309\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(2\) \(-\) \(-\) \(q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
1792.2.a.r \(2\) \(14.309\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(2\) \(+\) \(-\) \(q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
1792.2.a.s \(2\) \(14.309\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-2\) \(-\) \(+\) \(q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots\)
1792.2.a.t \(2\) \(14.309\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(-2\) \(-\) \(+\) \(q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots\)
1792.2.a.u \(4\) \(14.309\) \(\Q(\zeta_{16})^+\) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(q+\beta _{1}q^{3}-\beta _{1}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
1792.2.a.v \(4\) \(14.309\) 4.4.9248.1 None \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(q+\beta _{2}q^{3}-\beta _{1}q^{5}-q^{7}+(2-\beta _{3})q^{9}+\cdots\)
1792.2.a.w \(4\) \(14.309\) \(\Q(\zeta_{16})^+\) None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
1792.2.a.x \(4\) \(14.309\) 4.4.9248.1 None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+q^{7}+(2-\beta _{3})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1792))\) into lower level spaces

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