↑

Properties

Label 354.3.f
Level $354$
Weight $3$
Character orbit 354.f
Rep. character $\chi_{354}(13,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $560$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 354.f (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{58})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(354, [\chi])\).

Total New Old
Modular forms 3472 560 2912
Cusp forms 3248 560 2688
Eisenstein series 224 0 224

Trace form

\( 560 q + 40 q^{4} - 8 q^{7} - 60 q^{9} + O(q^{10}) \) \( 560 q + 40 q^{4} - 8 q^{7} - 60 q^{9} + 24 q^{15} - 80 q^{16} - 72 q^{19} - 16 q^{22} - 140 q^{25} - 64 q^{26} + 16 q^{28} - 56 q^{29} + 80 q^{35} + 120 q^{36} + 8 q^{41} + 1376 q^{46} + 1276 q^{47} + 2036 q^{49} + 1856 q^{50} + 696 q^{52} + 1128 q^{53} + 1044 q^{55} + 48 q^{57} - 424 q^{59} - 48 q^{60} - 696 q^{61} - 448 q^{62} - 24 q^{63} + 160 q^{64} - 2436 q^{65} - 96 q^{66} - 2088 q^{67} - 1160 q^{68} - 2784 q^{70} - 2448 q^{71} - 1740 q^{73} - 1568 q^{74} + 96 q^{75} + 144 q^{76} - 192 q^{78} - 528 q^{79} - 180 q^{81} - 568 q^{85} + 416 q^{86} + 216 q^{87} + 32 q^{88} + 480 q^{94} + 456 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(354, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
354.3.f.a 354.f 59.d $560$ $9.646$ None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{58}]$

Decomposition of \(S_{3}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(118, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)