Properties

Label 784.2.p
Level $784$
Weight $2$
Character orbit 784.p
Rep. character $\chi_{784}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $10$
Sturm bound $224$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(224\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(784, [\chi])\).

Total New Old
Modular forms 272 40 232
Cusp forms 176 40 136
Eisenstein series 96 0 96

Trace form

\( 40q - 20q^{9} + O(q^{10}) \) \( 40q - 20q^{9} + 32q^{25} + 24q^{29} + 36q^{33} + 4q^{37} - 36q^{45} - 12q^{53} - 104q^{57} - 36q^{61} + 36q^{65} + 12q^{73} - 56q^{81} + 120q^{85} + 36q^{89} - 28q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
784.2.p.a \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-6\) \(0\) \(q+(-2+2\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+\cdots\)
784.2.p.b \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(6\) \(0\) \(q+(-2+2\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
784.2.p.c \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(0\) \(q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
784.2.p.d \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(0\) \(q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
784.2.p.e \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-6\) \(0\) \(q+(2-2\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
784.2.p.f \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(6\) \(0\) \(q+(2-2\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
784.2.p.g \(4\) \(6.260\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(6\) \(0\) \(q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+4\beta _{2}q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
784.2.p.h \(8\) \(6.260\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}-\beta _{5})q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-3+\cdots)q^{9}+\cdots\)
784.2.p.i \(8\) \(6.260\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}-\beta _{5})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(-3+\cdots)q^{9}+\cdots\)
784.2.p.j \(8\) \(6.260\) 8.0.339738624.1 \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}+3\beta _{4}q^{9}+(\beta _{1}+\beta _{3}+\beta _{6}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(784, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 3}\)