Properties

Label 1232.2.q
Level $1232$
Weight $2$
Character orbit 1232.q
Rep. character $\chi_{1232}(177,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $16$
Sturm bound $384$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1232.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 16 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1232, [\chi])\).

Total New Old
Modular forms 408 80 328
Cusp forms 360 80 280
Eisenstein series 48 0 48

Trace form

\( 80 q - 4 q^{3} - 4 q^{7} - 40 q^{9} + O(q^{10}) \) \( 80 q - 4 q^{3} - 4 q^{7} - 40 q^{9} + 4 q^{19} + 8 q^{21} - 40 q^{25} + 32 q^{27} + 16 q^{29} + 28 q^{31} + 12 q^{35} + 4 q^{39} - 32 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 20 q^{51} - 16 q^{55} - 48 q^{57} - 44 q^{59} - 92 q^{63} + 16 q^{65} - 8 q^{67} - 32 q^{69} + 16 q^{71} + 8 q^{73} + 8 q^{75} + 28 q^{79} - 16 q^{81} + 40 q^{83} + 8 q^{89} + 48 q^{91} + 32 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1232, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1232.2.q.a 1232.q 7.c $2$ $9.838$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(4\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1232.2.q.b 1232.q 7.c $2$ $9.838$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1232.2.q.c 1232.q 7.c $2$ $9.838$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
1232.2.q.d 1232.q 7.c $2$ $9.838$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
1232.2.q.e 1232.q 7.c $2$ $9.838$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1232.2.q.f 1232.q 7.c $4$ $9.838$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
1232.2.q.g 1232.q 7.c $4$ $9.838$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1232.2.q.h 1232.q 7.c $4$ $9.838$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
1232.2.q.i 1232.q 7.c $6$ $9.838$ 6.0.64827.1 None \(0\) \(-5\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+(1+\cdots)q^{5}+\cdots\)
1232.2.q.j 1232.q 7.c $6$ $9.838$ 6.0.1783323.2 None \(0\) \(-3\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{4}-\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
1232.2.q.k 1232.q 7.c $6$ $9.838$ 6.0.1783323.2 None \(0\) \(-1\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
1232.2.q.l 1232.q 7.c $6$ $9.838$ 6.0.309123.1 None \(0\) \(1\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{5}+\cdots\)
1232.2.q.m 1232.q 7.c $6$ $9.838$ \(\Q(\zeta_{18})\) None \(0\) \(3\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+(-\zeta_{18}+\cdots)q^{5}+\cdots\)
1232.2.q.n 1232.q 7.c $8$ $9.838$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-2\) \(4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}-\beta _{4})q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
1232.2.q.o 1232.q 7.c $10$ $9.838$ 10.0.\(\cdots\).1 None \(0\) \(-1\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}+\beta _{8})q^{3}+(-1+\beta _{3}+\beta _{4}+\beta _{7}+\cdots)q^{5}+\cdots\)
1232.2.q.p 1232.q 7.c $10$ $9.838$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(3\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}-\beta _{7})q^{3}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1232, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1232, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 2}\)