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Properties

Label 354.5.b
Level $354$
Weight $5$
Character orbit 354.b
Rep. character $\chi_{354}(119,\cdot)$
Character field $\Q$
Dimension $76$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
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 76 168
Cusp forms 236 76 160
Eisenstein series 8 0 8

Trace form

\( 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9} + O(q^{10}) \) \( 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9} + 256 q^{10} - 200 q^{13} - 26 q^{15} + 4864 q^{16} - 512 q^{18} + 616 q^{19} + 330 q^{21} + 640 q^{22} + 512 q^{24} - 10540 q^{25} - 354 q^{27} + 1472 q^{28} - 832 q^{30} - 3920 q^{31} - 188 q^{33} + 2560 q^{34} - 1344 q^{36} - 1440 q^{37} + 8204 q^{39} - 2048 q^{40} - 5760 q^{42} - 1944 q^{43} + 3886 q^{45} + 4864 q^{46} + 33636 q^{49} - 7544 q^{51} + 1600 q^{52} + 3392 q^{54} - 10536 q^{55} - 12182 q^{57} - 7168 q^{58} + 208 q^{60} + 6360 q^{61} + 10860 q^{63} - 38912 q^{64} + 19712 q^{66} + 30744 q^{67} - 34208 q^{69} - 23808 q^{70} + 4096 q^{72} + 4032 q^{73} + 22324 q^{75} - 4928 q^{76} + 12864 q^{78} - 29824 q^{79} - 22584 q^{81} + 13184 q^{82} - 2640 q^{84} + 9240 q^{85} + 32850 q^{87} - 5120 q^{88} - 16448 q^{90} - 31160 q^{91} - 1780 q^{93} + 5248 q^{94} - 4096 q^{96} + 77504 q^{97} - 15412 q^{99} + O(q^{100}) \)

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.b.a 354.b 3.b $76$ $36.593$ None \(0\) \(0\) \(0\) \(-184\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{5}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)