Properties

Label 464.2.u
Level $464$
Weight $2$
Character orbit 464.u
Rep. character $\chi_{464}(49,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $84$
Newform subspaces $9$
Sturm bound $120$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 464 = 2^{4} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 464.u (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 9 \)
Sturm bound: \(120\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(464, [\chi])\).

Total New Old
Modular forms 396 96 300
Cusp forms 324 84 240
Eisenstein series 72 12 60

Trace form

\( 84 q + 5 q^{3} - 7 q^{5} + 3 q^{7} - 17 q^{9} + O(q^{10}) \) \( 84 q + 5 q^{3} - 7 q^{5} + 3 q^{7} - 17 q^{9} + 15 q^{11} - 7 q^{13} - q^{15} - 10 q^{17} + 5 q^{19} - 7 q^{21} - 5 q^{23} + 7 q^{25} - 13 q^{27} - 7 q^{29} + 5 q^{31} - 7 q^{33} + 7 q^{35} - 7 q^{37} + 53 q^{39} - 10 q^{41} + q^{43} + 28 q^{45} + 5 q^{47} - 21 q^{49} + 56 q^{51} + 19 q^{55} - 6 q^{57} - 108 q^{59} - 23 q^{61} + 11 q^{63} + 10 q^{65} + 15 q^{67} - 7 q^{69} + 23 q^{71} - 38 q^{73} + 4 q^{75} + 9 q^{77} + 55 q^{79} + 3 q^{81} + 35 q^{83} - 42 q^{85} - 71 q^{87} + 5 q^{89} - 9 q^{91} - 59 q^{93} + 55 q^{95} - 10 q^{97} - 140 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(464, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
464.2.u.a 464.u 29.d $6$ $3.705$ \(\Q(\zeta_{14})\) None 232.2.m.c \(0\) \(-5\) \(7\) \(3\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1+\zeta_{14}^{5})q^{3}+(1-\zeta_{14}-2\zeta_{14}^{4}+\cdots)q^{5}+\cdots\)
464.2.u.b 464.u 29.d $6$ $3.705$ \(\Q(\zeta_{14})\) None 58.2.d.a \(0\) \(-3\) \(-4\) \(5\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{3}+\cdots\)
464.2.u.c 464.u 29.d $6$ $3.705$ \(\Q(\zeta_{14})\) None 116.2.g.a \(0\) \(-3\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1-2\zeta_{14}+2\zeta_{14}^{2}-2\zeta_{14}^{3}+2\zeta_{14}^{4}+\cdots)q^{3}+\cdots\)
464.2.u.d 464.u 29.d $6$ $3.705$ \(\Q(\zeta_{14})\) None 232.2.m.b \(0\) \(1\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1+2\zeta_{14}^{2}-2\zeta_{14}^{3}-\zeta_{14}^{5})q^{3}+\cdots\)
464.2.u.e 464.u 29.d $6$ $3.705$ \(\Q(\zeta_{14})\) None 232.2.m.a \(0\) \(3\) \(2\) \(3\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1-\zeta_{14}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{3}+(\zeta_{14}^{3}+\cdots)q^{5}+\cdots\)
464.2.u.f 464.u 29.d $6$ $3.705$ \(\Q(\zeta_{14})\) None 29.2.d.a \(0\) \(5\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1-\zeta_{14}^{5})q^{3}+(1-\zeta_{14}-2\zeta_{14}^{3}+\cdots)q^{5}+\cdots\)
464.2.u.g 464.u 29.d $12$ $3.705$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 116.2.g.b \(0\) \(3\) \(-1\) \(7\) $\mathrm{SU}(2)[C_{7}]$ \(q+(\beta _{1}+\beta _{8})q^{3}+(-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
464.2.u.h 464.u 29.d $12$ $3.705$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 58.2.d.b \(0\) \(3\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{7}]$ \(q-\beta _{11}q^{3}+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots\)
464.2.u.i 464.u 29.d $24$ $3.705$ None 232.2.m.d \(0\) \(1\) \(-8\) \(-5\) $\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{2}^{\mathrm{old}}(464, [\chi])\) into lower level spaces

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