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Properties

Label 350.3.n
Level $350$
Weight $3$
Character orbit 350.n
Rep. character $\chi_{350}(41,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $160$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 350.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(350, [\chi])\).

Total New Old
Modular forms 496 160 336
Cusp forms 464 160 304
Eisenstein series 32 0 32

Trace form

\( 160 q - 80 q^{4} + 4 q^{7} + 120 q^{9} + O(q^{10}) \) \( 160 q - 80 q^{4} + 4 q^{7} + 120 q^{9} + 60 q^{11} + 20 q^{15} - 160 q^{16} - 32 q^{18} + 60 q^{21} + 88 q^{22} + 12 q^{23} + 40 q^{25} + 48 q^{28} - 60 q^{29} - 80 q^{30} + 70 q^{35} + 240 q^{36} - 136 q^{37} - 320 q^{39} - 200 q^{42} + 352 q^{43} - 80 q^{44} - 120 q^{46} + 140 q^{49} - 240 q^{51} + 588 q^{53} - 1256 q^{57} + 224 q^{58} + 200 q^{60} + 620 q^{63} - 320 q^{64} + 100 q^{65} + 112 q^{67} + 420 q^{70} - 460 q^{71} - 64 q^{72} + 160 q^{74} + 168 q^{77} - 320 q^{78} - 440 q^{79} - 800 q^{81} - 180 q^{84} + 640 q^{85} - 240 q^{86} - 224 q^{88} - 200 q^{91} - 96 q^{92} + 584 q^{93} - 220 q^{95} + 112 q^{98} + 760 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
350.3.n.a 350.n 175.l $160$ $9.537$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{3}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)