Properties

Label 1176.2.q
Level $1176$
Weight $2$
Character orbit 1176.q
Rep. character $\chi_{1176}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $40$
Newform subspaces $15$
Sturm bound $448$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1176.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 15 \)
Sturm bound: \(448\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1176, [\chi])\).

Total New Old
Modular forms 512 40 472
Cusp forms 384 40 344
Eisenstein series 128 0 128

Trace form

\( 40q - 2q^{3} - 20q^{9} + O(q^{10}) \) \( 40q - 2q^{3} - 20q^{9} - 4q^{11} - 12q^{13} + 4q^{15} - 4q^{17} - 14q^{19} + 12q^{23} - 6q^{25} + 4q^{27} + 8q^{29} + 10q^{33} + 6q^{37} + 2q^{39} - 24q^{41} - 4q^{43} + 8q^{51} - 12q^{53} - 28q^{55} - 20q^{57} + 20q^{61} - 24q^{65} + 2q^{67} - 8q^{69} - 32q^{71} - 10q^{73} - 22q^{75} + 28q^{79} - 20q^{81} - 40q^{83} + 72q^{85} - 2q^{87} - 32q^{89} - 22q^{93} - 48q^{95} + 12q^{97} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1176.2.q.a \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1176.2.q.b \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1176.2.q.c \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+4q^{13}+(-4+\cdots)q^{17}+\cdots\)
1176.2.q.d \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1176.2.q.e \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1176.2.q.f \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+6q^{13}+\cdots\)
1176.2.q.g \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
1176.2.q.h \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}-4q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
1176.2.q.i \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
1176.2.q.j \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+2q^{13}+\cdots\)
1176.2.q.k \(4\) \(9.390\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(-4\) \(0\) \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
1176.2.q.l \(4\) \(9.390\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(-2\) \(-1\) \(0\) \(q+\beta _{1}q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{9}+\cdots\)
1176.2.q.m \(4\) \(9.390\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(4\) \(0\) \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
1176.2.q.n \(4\) \(9.390\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-4\) \(0\) \(q+(1+\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
1176.2.q.o \(4\) \(9.390\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(4\) \(0\) \(q+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1176, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)