Properties

Label 1764.3.c
Level $1764$
Weight $3$
Character orbit 1764.c
Rep. character $\chi_{1764}(197,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $8$
Sturm bound $1008$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1764.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(1008\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1764, [\chi])\).

Total New Old
Modular forms 720 28 692
Cusp forms 624 28 596
Eisenstein series 96 0 96

Trace form

\( 28 q + O(q^{10}) \) \( 28 q + 8 q^{13} + 40 q^{19} - 228 q^{25} - 40 q^{31} + 4 q^{37} + 172 q^{43} + 104 q^{55} + 272 q^{61} + 60 q^{67} - 144 q^{73} - 596 q^{79} + 160 q^{85} - 96 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1764.3.c.a \(2\) \(48.066\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-5\beta q^{11}-23q^{13}+4\beta q^{17}+\cdots\)
1764.3.c.b \(2\) \(48.066\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4\beta q^{5}+\beta q^{11}-2^{4}q^{13}-12\beta q^{17}+\cdots\)
1764.3.c.c \(2\) \(48.066\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4\beta q^{5}-\beta q^{11}+2^{4}q^{13}-12\beta q^{17}+\cdots\)
1764.3.c.d \(2\) \(48.066\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}+5\beta q^{11}+23q^{13}+4\beta q^{17}+\cdots\)
1764.3.c.e \(4\) \(48.066\) \(\Q(\sqrt{-2}, \sqrt{-23})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{3})q^{11}+(-14+\cdots)q^{13}+\cdots\)
1764.3.c.f \(4\) \(48.066\) \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+(-2\beta _{1}-\beta _{2})q^{11}+(2-2\beta _{3})q^{13}+\cdots\)
1764.3.c.g \(4\) \(48.066\) \(\Q(\sqrt{-2}, \sqrt{-23})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{5}+(-2\beta _{1}-\beta _{3})q^{11}+\cdots\)
1764.3.c.h \(8\) \(48.066\) 8.0.\(\cdots\).12 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+\beta _{5}q^{11}+3\beta _{3}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)