Properties

Label 784.2.i
Level $784$
Weight $2$
Character orbit 784.i
Rep. character $\chi_{784}(177,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $36$
Newform subspaces $14$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
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 44 228
Cusp forms 176 36 140
Eisenstein series 96 8 88

Trace form

\( 36q - 3q^{3} + q^{5} - 13q^{9} + O(q^{10}) \) \( 36q - 3q^{3} + q^{5} - 13q^{9} + 3q^{11} + 4q^{13} + 14q^{15} + q^{17} - 5q^{19} + 9q^{23} - 13q^{25} + 18q^{27} + 16q^{29} + 13q^{31} - 9q^{33} - 7q^{37} - 26q^{39} + 12q^{41} - 16q^{43} - 10q^{45} + 3q^{47} - 47q^{51} - 11q^{53} - 22q^{55} - 54q^{57} - 27q^{59} - 3q^{61} + 18q^{65} + 15q^{67} - 2q^{69} + 64q^{71} + 13q^{73} + 4q^{75} + 33q^{79} + 22q^{81} + 40q^{83} - 50q^{85} + 26q^{87} + 13q^{89} + 21q^{93} - 33q^{95} + 12q^{97} + 4q^{99} + O(q^{100}) \)

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.i.a \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-1\) \(0\) \(q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
784.2.i.b \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-4\) \(0\) \(q+(-2+2\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
784.2.i.c \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{9}-4q^{13}+\cdots\)
784.2.i.d \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(0\) \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
784.2.i.e \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots\)
784.2.i.f \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+8\zeta_{6}q^{23}+\cdots\)
784.2.i.g \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots\)
784.2.i.h \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots\)
784.2.i.i \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{9}+4q^{13}+(6+\cdots)q^{17}+\cdots\)
784.2.i.j \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(4\) \(0\) \(q+(2-2\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+8q^{15}+\cdots\)
784.2.i.k \(4\) \(6.260\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+5\beta _{2}q^{9}+(-4+\cdots)q^{11}+\cdots\)
784.2.i.l \(4\) \(6.260\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots\)
784.2.i.m \(4\) \(6.260\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-2\beta _{1}-2\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots\)
784.2.i.n \(4\) \(6.260\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(2\beta _{1}+2\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)