Properties

Label 1792.2.m
Level $1792$
Weight $2$
Character orbit 1792.m
Rep. character $\chi_{1792}(449,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $8$
Sturm bound $512$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 8 \)
Sturm bound: \(512\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 560 96 464
Cusp forms 464 96 368
Eisenstein series 96 0 96

Trace form

\( 96q + O(q^{10}) \) \( 96q - 96q^{49} + 192q^{65} - 96q^{81} + O(q^{100}) \)

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.m.a \(8\) \(14.309\) 8.0.18939904.2 None \(0\) \(-4\) \(-4\) \(0\) \(q-\beta _{3}q^{3}+(-1-\beta _{4}+\beta _{6}+\beta _{7})q^{5}+\cdots\)
1792.2.m.b \(8\) \(14.309\) 8.0.18939904.2 None \(0\) \(-4\) \(4\) \(0\) \(q-\beta _{3}q^{3}+(1+\beta _{4}-\beta _{6}-\beta _{7})q^{5}+\beta _{6}q^{7}+\cdots\)
1792.2.m.c \(8\) \(14.309\) 8.0.18939904.2 None \(0\) \(4\) \(-4\) \(0\) \(q+\beta _{3}q^{3}+(-1-\beta _{4}+\beta _{6}+\beta _{7})q^{5}+\cdots\)
1792.2.m.d \(8\) \(14.309\) 8.0.18939904.2 None \(0\) \(4\) \(4\) \(0\) \(q+\beta _{3}q^{3}+(1+\beta _{4}-\beta _{6}-\beta _{7})q^{5}-\beta _{6}q^{7}+\cdots\)
1792.2.m.e \(16\) \(14.309\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-4\) \(-4\) \(0\) \(q-\beta _{11}q^{3}+\beta _{10}q^{5}+\beta _{5}q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots\)
1792.2.m.f \(16\) \(14.309\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-4\) \(4\) \(0\) \(q-\beta _{11}q^{3}-\beta _{10}q^{5}-\beta _{5}q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots\)
1792.2.m.g \(16\) \(14.309\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(4\) \(-4\) \(0\) \(q+\beta _{11}q^{3}+\beta _{10}q^{5}-\beta _{5}q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots\)
1792.2.m.h \(16\) \(14.309\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(4\) \(4\) \(0\) \(q+\beta _{11}q^{3}-\beta _{10}q^{5}+\beta _{5}q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1792, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 2}\)