Properties

Label 576.3.g
Level $576$
Weight $3$
Character orbit 576.g
Rep. character $\chi_{576}(127,\cdot)$
Character field $\Q$
Dimension $19$
Newform subspaces $10$
Sturm bound $288$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 576.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(576, [\chi])\).

Total New Old
Modular forms 216 21 195
Cusp forms 168 19 149
Eisenstein series 48 2 46

Trace form

\( 19 q - 2 q^{5} + O(q^{10}) \) \( 19 q - 2 q^{5} - 14 q^{13} + 10 q^{17} + 49 q^{25} - 18 q^{29} - 30 q^{37} + 90 q^{41} - 93 q^{49} + 62 q^{53} + 146 q^{61} - 12 q^{65} + 22 q^{73} + 256 q^{77} + 68 q^{85} + 58 q^{89} + 38 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
576.3.g.a \(1\) \(15.695\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-8\) \(0\) \(q-8q^{5}+10q^{13}-2^{4}q^{17}+39q^{25}+\cdots\)
576.3.g.b \(1\) \(15.695\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) \(q-6q^{5}-10q^{13}+30q^{17}+11q^{25}+\cdots\)
576.3.g.c \(1\) \(15.695\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(8\) \(0\) \(q+8q^{5}+10q^{13}+2^{4}q^{17}+39q^{25}+\cdots\)
576.3.g.d \(2\) \(15.695\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-8\) \(0\) \(q-4q^{5}+iq^{7}-4iq^{11}+2q^{13}+24q^{17}+\cdots\)
576.3.g.e \(2\) \(15.695\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-2q^{5}-\zeta_{6}q^{7}+\zeta_{6}q^{11}-2q^{13}+\cdots\)
576.3.g.f \(2\) \(15.695\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{7}-22q^{13}+2\zeta_{6}q^{19}-5^{2}q^{25}+\cdots\)
576.3.g.g \(2\) \(15.695\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+2q^{5}+2iq^{7}+iq^{11}+14q^{13}+\cdots\)
576.3.g.h \(2\) \(15.695\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(8\) \(0\) \(q+4q^{5}+iq^{7}+4iq^{11}+2q^{13}-24q^{17}+\cdots\)
576.3.g.i \(2\) \(15.695\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(12\) \(0\) \(q+6q^{5}-\zeta_{6}q^{7}+3\zeta_{6}q^{11}+14q^{13}+\cdots\)
576.3.g.j \(4\) \(15.695\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-2+\zeta_{12}^{2})q^{5}+(\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)