Properties

Label 2592.2.s
Level $2592$
Weight $2$
Character orbit 2592.s
Rep. character $\chi_{2592}(863,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $10$
Sturm bound $864$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2592.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(864\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2592, [\chi])\).

Total New Old
Modular forms 960 96 864
Cusp forms 768 96 672
Eisenstein series 192 0 192

Trace form

\( 96 q + O(q^{10}) \) \( 96 q + 48 q^{25} + 48 q^{49} - 48 q^{73} - 24 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2592, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2592.2.s.a \(8\) \(20.697\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-12\) \(0\) \(q+(-2+\zeta_{24}^{2}+\zeta_{24}^{5})q^{5}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{7}+\cdots\)
2592.2.s.b \(8\) \(20.697\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-12\) \(q+(\zeta_{24}-\zeta_{24}^{5}+\zeta_{24}^{7})q^{5}+(-2-\zeta_{24}^{2}+\cdots)q^{7}+\cdots\)
2592.2.s.c \(8\) \(20.697\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-12\) \(q+\zeta_{24}^{6}q^{5}+(-2+\zeta_{24}+\zeta_{24}^{2}-\zeta_{24}^{4}+\cdots)q^{7}+\cdots\)
2592.2.s.d \(8\) \(20.697\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{4}q^{5}+\zeta_{24}q^{7}+(-\zeta_{24}^{6}+\zeta_{24}^{7})q^{11}+\cdots\)
2592.2.s.e \(8\) \(20.697\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{5}q^{5}-\zeta_{24}q^{7}+(\zeta_{24}^{4}-\zeta_{24}^{7})q^{11}+\cdots\)
2592.2.s.f \(8\) \(20.697\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(12\) \(q+(\zeta_{24}-\zeta_{24}^{5}+\zeta_{24}^{7})q^{5}+(2+\zeta_{24}^{2}+\cdots)q^{7}+\cdots\)
2592.2.s.g \(8\) \(20.697\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(12\) \(q+\zeta_{24}^{6}q^{5}+(2-\zeta_{24}-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{7}+\cdots\)
2592.2.s.h \(8\) \(20.697\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(12\) \(0\) \(q+(2-\zeta_{24}^{2}-\zeta_{24}^{5})q^{5}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{7}+\cdots\)
2592.2.s.i \(16\) \(20.697\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-12\) \(q+(-\beta _{5}-\beta _{9}+\beta _{12}+\beta _{14}+\beta _{15})q^{5}+\cdots\)
2592.2.s.j \(16\) \(20.697\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(12\) \(q+(-\beta _{5}-\beta _{9}+\beta _{12}+\beta _{14}+\beta _{15})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2592, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2592, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 2}\)