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 $7$

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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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1232.2.q.a \(2\) \(9.838\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(4\) \(5\) \(q+(-3+3\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1232.2.q.b \(2\) \(9.838\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(-5\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1232.2.q.c \(2\) \(9.838\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-5\) \(q+(1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
1232.2.q.d \(2\) \(9.838\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q+(1-\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
1232.2.q.e \(2\) \(9.838\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-2\) \(5\) \(q+(3-3\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1232.2.q.f \(4\) \(9.838\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(4\) \(2\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
1232.2.q.g \(4\) \(9.838\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1232.2.q.h \(4\) \(9.838\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(0\) \(-2\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
1232.2.q.i \(6\) \(9.838\) 6.0.64827.1 None \(0\) \(-5\) \(2\) \(0\) \(q+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+(1+\cdots)q^{5}+\cdots\)
1232.2.q.j \(6\) \(9.838\) 6.0.1783323.2 None \(0\) \(-3\) \(2\) \(-2\) \(q+(-1+\beta _{4}-\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
1232.2.q.k \(6\) \(9.838\) 6.0.1783323.2 None \(0\) \(-1\) \(2\) \(-2\) \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
1232.2.q.l \(6\) \(9.838\) 6.0.309123.1 None \(0\) \(1\) \(2\) \(-4\) \(q+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{5}+\cdots\)
1232.2.q.m \(6\) \(9.838\) \(\Q(\zeta_{18})\) None \(0\) \(3\) \(-6\) \(0\) \(q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+(-\zeta_{18}+\cdots)q^{5}+\cdots\)
1232.2.q.n \(8\) \(9.838\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-2\) \(4\) \(1\) \(q+(\beta _{2}-\beta _{4})q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
1232.2.q.o \(10\) \(9.838\) 10.0.\(\cdots\).1 None \(0\) \(-1\) \(-4\) \(2\) \(q+(\beta _{2}+\beta _{8})q^{3}+(-1+\beta _{3}+\beta _{4}+\beta _{7}+\cdots)q^{5}+\cdots\)
1232.2.q.p \(10\) \(9.838\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(3\) \(-4\) \(0\) \(q+(-\beta _{4}-\beta _{7})q^{3}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

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

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