Properties

Label 624.3.ba
Level $624$
Weight $3$
Character orbit 624.ba
Rep. character $\chi_{624}(385,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $6$
Sturm bound $336$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 624.ba (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(336\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(624, [\chi])\).

Total New Old
Modular forms 472 56 416
Cusp forms 424 56 368
Eisenstein series 48 0 48

Trace form

\( 56 q + 8 q^{5} + 16 q^{7} + 168 q^{9} - 32 q^{19} - 16 q^{31} + 8 q^{37} - 48 q^{39} - 72 q^{41} + 24 q^{45} - 96 q^{47} + 80 q^{53} + 320 q^{55} + 48 q^{57} + 64 q^{59} - 176 q^{61} + 48 q^{63} + 216 q^{65}+ \cdots + 280 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(624, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
624.3.ba.a 624.ba 13.d $4$ $17.003$ \(\Q(\zeta_{12})\) None 78.3.f.a \(0\) \(0\) \(12\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta_{3} q^{3}+(-\beta_{3}+\beta_{2}-3\beta_1+3)q^{5}+\cdots\)
624.3.ba.b 624.ba 13.d $8$ $17.003$ 8.0.\(\cdots\).10 None 39.3.g.a \(0\) \(0\) \(-20\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(-3+\beta _{2}+3\beta _{5}+\beta _{6})q^{5}+\cdots\)
624.3.ba.c 624.ba 13.d $8$ $17.003$ 8.0.\(\cdots\).1 None 78.3.f.b \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
624.3.ba.d 624.ba 13.d $8$ $17.003$ 8.0.\(\cdots\).10 None 156.3.j.a \(0\) \(0\) \(12\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{5}+(2+\cdots)q^{7}+\cdots\)
624.3.ba.e 624.ba 13.d $12$ $17.003$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 312.3.s.a \(0\) \(0\) \(8\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{3}+(1+\beta _{3}+\beta _{6})q^{5}+(1-\beta _{6}+\cdots)q^{7}+\cdots\)
624.3.ba.f 624.ba 13.d $16$ $17.003$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 312.3.s.b \(0\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{3}-\beta _{2}q^{5}+\beta _{11}q^{7}+3q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(624, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(624, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)