Properties

Label 3456.2.i
Level $3456$
Weight $2$
Character orbit 3456.i
Rep. character $\chi_{3456}(1153,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $96$
Newform subspaces $12$
Sturm bound $1152$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3456 = 2^{7} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3456.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(1152\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3456, [\chi])\).

Total New Old
Modular forms 1248 96 1152
Cusp forms 1056 96 960
Eisenstein series 192 0 192

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(3456, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3456.2.i.a $2$ $27.596$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-2\) \(q-2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
3456.2.i.b $2$ $27.596$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(2\) \(q-2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
3456.2.i.c $2$ $27.596$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-2\) \(q+2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
3456.2.i.d $2$ $27.596$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(2\) \(q+2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
3456.2.i.e $10$ $27.596$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-4\) \(q+(-\beta _{2}+\beta _{8}+\beta _{9})q^{5}+(\beta _{1}+\beta _{9})q^{7}+\cdots\)
3456.2.i.f $10$ $27.596$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-4\) \(q+(\beta _{2}-\beta _{8}-\beta _{9})q^{5}+(\beta _{1}+\beta _{9})q^{7}+\cdots\)
3456.2.i.g $10$ $27.596$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(4\) \(q+(\beta _{2}-\beta _{8}-\beta _{9})q^{5}+(-\beta _{1}-\beta _{9})q^{7}+\cdots\)
3456.2.i.h $10$ $27.596$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(4\) \(q+(-\beta _{2}+\beta _{8}+\beta _{9})q^{5}+(-\beta _{1}-\beta _{9})q^{7}+\cdots\)
3456.2.i.i $12$ $27.596$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-2\) \(-6\) \(q+\beta _{6}q^{5}+(-1+\beta _{7}+\beta _{10})q^{7}+(-1+\cdots)q^{11}+\cdots\)
3456.2.i.j $12$ $27.596$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-2\) \(6\) \(q+\beta _{6}q^{5}+(1-\beta _{7}-\beta _{10})q^{7}+(1-\beta _{7}+\cdots)q^{11}+\cdots\)
3456.2.i.k $12$ $27.596$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(2\) \(-6\) \(q-\beta _{6}q^{5}+(-1+\beta _{7}+\beta _{10})q^{7}+(1+\cdots)q^{11}+\cdots\)
3456.2.i.l $12$ $27.596$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(2\) \(6\) \(q-\beta _{6}q^{5}+(1-\beta _{7}-\beta _{10})q^{7}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1728, [\chi])\)\(^{\oplus 2}\)