↑

Properties

Label 1152.2.i
Level $1152$
Weight $2$
Character orbit 1152.i
Rep. character $\chi_{1152}(385,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $96$
Newform subspaces $12$
Sturm bound $384$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1152, [\chi])\).

Total New Old
Modular forms 416 96 320
Cusp forms 352 96 256
Eisenstein series 64 0 64

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 48 q^{25} - 32 q^{33} - 16 q^{41} - 48 q^{49} + 16 q^{57} + 48 q^{81} + 64 q^{89} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1152.2.i.a 1152.i 9.c $2$ $9.199$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
1152.2.i.b 1152.i 9.c $2$ $9.199$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
1152.2.i.c 1152.i 9.c $2$ $9.199$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
1152.2.i.d 1152.i 9.c $2$ $9.199$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
1152.2.i.e 1152.i 9.c $10$ $9.199$ 10.0.\(\cdots\).1 None \(0\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{5}-\beta _{7})q^{3}-\beta _{8}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
1152.2.i.f 1152.i 9.c $10$ $9.199$ 10.0.\(\cdots\).1 None \(0\) \(-1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{5}-\beta _{7})q^{3}+\beta _{8}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
1152.2.i.g 1152.i 9.c $10$ $9.199$ 10.0.\(\cdots\).1 None \(0\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{5}+\beta _{7})q^{3}+\beta _{8}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
1152.2.i.h 1152.i 9.c $10$ $9.199$ 10.0.\(\cdots\).1 None \(0\) \(1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{5}+\beta _{7})q^{3}-\beta _{8}q^{5}+(1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1152.2.i.i 1152.i 9.c $12$ $9.199$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-4\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{6})q^{3}+(\beta _{4}-\beta _{5}-\beta _{6})q^{5}+\cdots\)
1152.2.i.j 1152.i 9.c $12$ $9.199$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-4\) \(2\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{6})q^{3}+(-\beta _{4}+\beta _{5}+\beta _{6})q^{5}+\cdots\)
1152.2.i.k 1152.i 9.c $12$ $9.199$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(4\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{6})q^{3}+(\beta _{4}-\beta _{5}-\beta _{6})q^{5}+\cdots\)
1152.2.i.l 1152.i 9.c $12$ $9.199$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(4\) \(2\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{6})q^{3}+(-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)