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Properties

Label 464.3.l
Level $464$
Weight $3$
Character orbit 464.l
Rep. character $\chi_{464}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $58$
Newform subspaces $6$
Sturm bound $180$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 464 = 2^{4} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 464.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(180\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(464, [\chi])\).

Total New Old
Modular forms 252 62 190
Cusp forms 228 58 170
Eisenstein series 24 4 20

Trace form

\( 58 q + 2 q^{3} + 4 q^{7} + O(q^{10}) \) \( 58 q + 2 q^{3} + 4 q^{7} + 18 q^{11} - 16 q^{15} - 6 q^{17} + 2 q^{19} - 36 q^{21} + 4 q^{23} - 230 q^{25} + 32 q^{27} - 50 q^{29} + 2 q^{31} + 66 q^{37} + 176 q^{39} - 22 q^{41} + 50 q^{43} + 96 q^{45} + 2 q^{47} + 478 q^{49} + 124 q^{53} - 144 q^{55} + 4 q^{59} + 146 q^{61} + 96 q^{65} - 132 q^{69} + 50 q^{73} - 430 q^{75} - 68 q^{77} + 162 q^{79} - 414 q^{81} + 4 q^{83} - 128 q^{85} + 338 q^{87} - 70 q^{89} - 576 q^{95} + 66 q^{97} + 254 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(464, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
464.3.l.a 464.l 29.c $4$ $12.643$ \(\Q(i, \sqrt{6})\) None \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)
464.3.l.b 464.l 29.c $6$ $12.643$ 6.0.9296045056.1 None \(0\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{3}+\beta _{4})q^{3}+(\beta _{4}-\beta _{5})q^{5}+(2+\cdots)q^{7}+\cdots\)
464.3.l.c 464.l 29.c $8$ $12.643$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{1}+\beta _{5})q^{3}+(\beta _{3}+\beta _{4})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
464.3.l.d 464.l 29.c $10$ $12.643$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(-\beta _{3}+\beta _{5})q^{5}-\beta _{6}q^{7}+\cdots\)
464.3.l.e 464.l 29.c $14$ $12.643$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{3}+(\beta _{4}-\beta _{7})q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
464.3.l.f 464.l 29.c $16$ $12.643$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{3}+(-\beta _{5}-\beta _{6})q^{5}+(1-\beta _{11}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(464, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(464, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 2}\)