Properties

Label 1792.2.b
Level $1792$
Weight $2$
Character orbit 1792.b
Rep. character $\chi_{1792}(897,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $16$
Sturm bound $512$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(512\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\), \(23\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1792, [\chi])\).

Total New Old
Modular forms 280 48 232
Cusp forms 232 48 184
Eisenstein series 48 0 48

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 \(S_{2}^{\mathrm{new}}(1792, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1792.2.b.a \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-8q^{15}+\cdots\)
1792.2.b.b \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}-q^{7}-q^{9}-2iq^{11}-2iq^{13}+\cdots\)
1792.2.b.c \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}-q^{7}-q^{9}+2iq^{13}+6q^{17}+\cdots\)
1792.2.b.d \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{5}-q^{7}+3q^{9}-2iq^{11}+iq^{13}+\cdots\)
1792.2.b.e \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+3q^{9}-iq^{11}+2iq^{13}-2q^{17}+\cdots\)
1792.2.b.f \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+q^{7}-q^{9}-2iq^{11}+2iq^{13}+\cdots\)
1792.2.b.g \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+q^{7}-q^{9}-2iq^{13}+6q^{17}+\cdots\)
1792.2.b.h \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}-2iq^{5}+q^{7}-q^{9}+8q^{15}+\cdots\)
1792.2.b.i \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{5}+q^{7}+3q^{9}+2iq^{11}+iq^{13}+\cdots\)
1792.2.b.j \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+q^{7}+3q^{9}+iq^{11}+2iq^{13}-2q^{17}+\cdots\)
1792.2.b.k \(4\) \(14.309\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-q^{7}+(-3+\cdots)q^{9}+\cdots\)
1792.2.b.l \(4\) \(14.309\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-q^{7}+(-1+\zeta_{12}^{3})q^{9}+\cdots\)
1792.2.b.m \(4\) \(14.309\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+q^{7}+(-3+\cdots)q^{9}+\cdots\)
1792.2.b.n \(4\) \(14.309\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+q^{7}+(-1+\zeta_{12}^{3})q^{9}+\cdots\)
1792.2.b.o \(6\) \(14.309\) 6.0.399424.1 None \(0\) \(0\) \(0\) \(-6\) \(q+\beta _{5}q^{3}+\beta _{4}q^{5}-q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots\)
1792.2.b.p \(6\) \(14.309\) 6.0.399424.1 None \(0\) \(0\) \(0\) \(6\) \(q+\beta _{5}q^{3}-\beta _{4}q^{5}+q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1792, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1792, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 2}\)