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Properties

Label 354.5.d
Level $354$
Weight $5$
Character orbit 354.d
Rep. character $\chi_{354}(235,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $1$
Sturm bound $300$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 354.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(300\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(354, [\chi])\).

Total New Old
Modular forms 244 40 204
Cusp forms 236 40 196
Eisenstein series 8 0 8

Trace form

\( 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9} + O(q^{10}) \) \( 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9} - 144 q^{15} + 2560 q^{16} + 480 q^{17} - 792 q^{19} - 1024 q^{22} + 3400 q^{25} + 768 q^{26} + 640 q^{28} + 1608 q^{29} - 5760 q^{35} - 8640 q^{36} + 6264 q^{41} + 7040 q^{46} + 17912 q^{49} + 1296 q^{51} - 1104 q^{53} + 5040 q^{57} + 13584 q^{59} + 1152 q^{60} - 12288 q^{62} - 2160 q^{63} - 20480 q^{64} + 1152 q^{66} - 3840 q^{68} + 35352 q^{71} + 4608 q^{74} + 3168 q^{75} + 6336 q^{76} - 12672 q^{78} - 15720 q^{79} + 29160 q^{81} - 26872 q^{85} + 18432 q^{86} + 7776 q^{87} + 8192 q^{88} - 18432 q^{94} - 19128 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(354, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
354.5.d.a 354.d 59.b $40$ $36.593$ None \(0\) \(0\) \(0\) \(-80\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(118, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)