Properties

Label 2352.3.f
Level $2352$
Weight $3$
Character orbit 2352.f
Rep. character $\chi_{2352}(97,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $13$
Sturm bound $1344$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2352.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(1344\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2352, [\chi])\).

Total New Old
Modular forms 944 80 864
Cusp forms 848 80 768
Eisenstein series 96 0 96

Trace form

\( 80 q - 240 q^{9} + O(q^{10}) \) \( 80 q - 240 q^{9} + 32 q^{11} + 160 q^{23} - 416 q^{25} - 32 q^{29} + 96 q^{37} - 48 q^{39} - 64 q^{43} + 128 q^{53} - 48 q^{57} + 160 q^{65} + 384 q^{67} - 128 q^{71} + 176 q^{79} + 720 q^{81} + 32 q^{85} - 96 q^{93} - 576 q^{95} - 96 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2352.3.f.a 2352.f 7.b $2$ $64.087$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{6}q^{3}-3\zeta_{6}q^{5}-3q^{9}-15q^{11}+\cdots\)
2352.3.f.b 2352.f 7.b $2$ $64.087$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}-2\zeta_{6}q^{5}-3q^{9}-10q^{11}+\cdots\)
2352.3.f.c 2352.f 7.b $2$ $64.087$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}-\zeta_{6}q^{5}-3q^{9}+3q^{11}-4\zeta_{6}q^{13}+\cdots\)
2352.3.f.d 2352.f 7.b $2$ $64.087$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{6}q^{3}-3\zeta_{6}q^{5}-3q^{9}+11q^{11}+\cdots\)
2352.3.f.e 2352.f 7.b $4$ $64.087$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{1}+2\beta _{2})q^{5}-3q^{9}+\cdots\)
2352.3.f.f 2352.f 7.b $4$ $64.087$ \(\Q(\sqrt{-3}, \sqrt{65})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2})q^{5}-3q^{9}+(8+\cdots)q^{11}+\cdots\)
2352.3.f.g 2352.f 7.b $8$ $64.087$ 8.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{7})q^{5}-3q^{9}+(-5+\cdots)q^{11}+\cdots\)
2352.3.f.h 2352.f 7.b $8$ $64.087$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+(2\beta _{2}-\beta _{5}-\beta _{7})q^{5}-3q^{9}+\cdots\)
2352.3.f.i 2352.f 7.b $8$ $64.087$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(-\beta _{4}-2\beta _{5})q^{5}-3q^{9}+\cdots\)
2352.3.f.j 2352.f 7.b $8$ $64.087$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{4}+\beta _{5})q^{5}-3q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
2352.3.f.k 2352.f 7.b $8$ $64.087$ 8.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{5})q^{5}-3q^{9}+(3+\cdots)q^{11}+\cdots\)
2352.3.f.l 2352.f 7.b $8$ $64.087$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{6}+\beta _{7})q^{5}-3q^{9}+(8+\cdots)q^{11}+\cdots\)
2352.3.f.m 2352.f 7.b $16$ $64.087$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-\beta _{2}+\beta _{11})q^{5}-3q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 20}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)