Properties

Label 2352.2.q
Level $2352$
Weight $2$
Character orbit 2352.q
Rep. character $\chi_{2352}(961,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $33$
Sturm bound $896$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 33 \)
Sturm bound: \(896\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

Total New Old
Modular forms 992 80 912
Cusp forms 800 80 720
Eisenstein series 192 0 192

Trace form

\( 80 q + 2 q^{3} - 40 q^{9} + O(q^{10}) \) \( 80 q + 2 q^{3} - 40 q^{9} - 8 q^{11} + 10 q^{19} - 20 q^{23} - 36 q^{25} - 4 q^{27} - 32 q^{29} - 14 q^{31} + 4 q^{33} + 16 q^{37} - 2 q^{39} - 16 q^{41} + 20 q^{43} + 12 q^{47} + 24 q^{53} + 56 q^{55} + 8 q^{57} + 16 q^{59} + 8 q^{61} + 8 q^{65} + 2 q^{67} - 16 q^{71} - 12 q^{73} + 14 q^{75} - 22 q^{79} - 40 q^{81} + 24 q^{83} + 32 q^{85} - 12 q^{87} - 16 q^{89} - 16 q^{93} + 60 q^{95} - 8 q^{97} + 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2352.2.q.a $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-4\) \(0\) \(q+(-1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.b $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-4\) \(0\) \(q+(-1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.c $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.d $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.e $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.f $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots\)
2352.2.q.g $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-6+6\zeta_{6})q^{11}+\cdots\)
2352.2.q.h $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}-4q^{13}+(4+\cdots)q^{17}+\cdots\)
2352.2.q.i $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.j $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.k $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.l $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.m $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(0\) \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.n $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
2352.2.q.o $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}-2q^{13}+\cdots\)
2352.2.q.p $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2352.2.q.q $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2352.2.q.r $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
2352.2.q.s $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-6+6\zeta_{6})q^{11}+\cdots\)
2352.2.q.t $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+4q^{13}+(-4+\cdots)q^{17}+\cdots\)
2352.2.q.u $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(0\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(5-5\zeta_{6})q^{11}+\cdots\)
2352.2.q.v $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
2352.2.q.w $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}-6q^{13}+\cdots\)
2352.2.q.x $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
2352.2.q.y $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(4\) \(0\) \(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
2352.2.q.z $2$ $18.781$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(4\) \(0\) \(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2352.2.q.ba $4$ $18.781$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(-4\) \(0\) \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bb $4$ $18.781$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(4\) \(0\) \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bc $4$ $18.781$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(4\) \(0\) \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bd $4$ $18.781$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-4\) \(0\) \(q+(1+\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.be $4$ $18.781$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-4\) \(0\) \(q+(1+\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bf $4$ $18.781$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(2\) \(-1\) \(0\) \(q-\beta _{1}q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{9}+\cdots\)
2352.2.q.bg $4$ $18.781$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(4\) \(0\) \(q+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)