Properties

Label 1728.4.c
Level $1728$
Weight $4$
Character orbit 1728.c
Rep. character $\chi_{1728}(1727,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $12$
Sturm bound $1152$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1728.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(1152\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1728, [\chi])\).

Total New Old
Modular forms 900 96 804
Cusp forms 828 96 732
Eisenstein series 72 0 72

Trace form

\( 96q + O(q^{10}) \) \( 96q - 72q^{13} - 2400q^{25} - 504q^{37} - 4704q^{49} - 168q^{61} + 240q^{85} - 1488q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1728.4.c.a \(2\) \(101.955\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-12\zeta_{6}q^{5}+17\zeta_{6}q^{7}-6^{2}q^{11}-19q^{13}+\cdots\)
1728.4.c.b \(2\) \(101.955\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{7}-19q^{13}-17\zeta_{6}q^{19}+5^{3}q^{25}+\cdots\)
1728.4.c.c \(2\) \(101.955\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+19\zeta_{6}q^{7}+89q^{13}+73\zeta_{6}q^{19}+\cdots\)
1728.4.c.d \(2\) \(101.955\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-12\zeta_{6}q^{5}-17\zeta_{6}q^{7}+6^{2}q^{11}-19q^{13}+\cdots\)
1728.4.c.e \(4\) \(101.955\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-6\zeta_{12}^{2})q^{5}+(-6\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
1728.4.c.f \(4\) \(101.955\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{5}+\zeta_{12}^{2}q^{7}+\zeta_{12}^{3}q^{11}+\cdots\)
1728.4.c.g \(4\) \(101.955\) \(\Q(\sqrt{3}, \sqrt{-17})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}-\beta _{3}q^{7}-\beta _{2}q^{11}+2q^{13}+\cdots\)
1728.4.c.h \(4\) \(101.955\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-6\zeta_{12}^{2})q^{5}+(6\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
1728.4.c.i \(12\) \(101.955\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{5}-\beta _{1}q^{7}+\beta _{5}q^{11}+(-3-\beta _{2}+\cdots)q^{13}+\cdots\)
1728.4.c.j \(12\) \(101.955\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}-\beta _{1}q^{7}-\beta _{6}q^{11}+(6-\beta _{5}+\cdots)q^{13}+\cdots\)
1728.4.c.k \(24\) \(101.955\) None \(0\) \(0\) \(0\) \(0\)
1728.4.c.l \(24\) \(101.955\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)