Properties

Label 350.3.w
Level $350$
Weight $3$
Character orbit 350.w
Rep. character $\chi_{350}(23,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $640$
Newform subspaces $2$
Sturm bound $180$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 350.w (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 2 \)
Sturm bound: \(180\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 1984 640 1344
Cusp forms 1856 640 1216
Eisenstein series 128 0 128

Trace form

\( 640 q - 4 q^{5} + 4 q^{7} + O(q^{10}) \) \( 640 q - 4 q^{5} + 4 q^{7} + 16 q^{10} + 72 q^{15} - 320 q^{16} + 188 q^{17} + 32 q^{18} - 64 q^{22} - 32 q^{23} + 4 q^{25} + 288 q^{27} - 16 q^{28} + 400 q^{29} - 144 q^{30} + 44 q^{33} - 452 q^{35} - 960 q^{36} + 28 q^{37} - 32 q^{38} + 400 q^{39} - 272 q^{42} + 200 q^{43} - 388 q^{45} - 220 q^{47} + 192 q^{50} - 524 q^{53} + 8 q^{55} - 488 q^{57} - 160 q^{58} + 400 q^{59} - 32 q^{60} + 1104 q^{62} + 1356 q^{63} - 20 q^{65} + 80 q^{67} - 176 q^{68} + 1400 q^{69} + 176 q^{70} + 64 q^{72} + 268 q^{73} - 304 q^{75} - 1156 q^{77} + 64 q^{78} + 16 q^{80} - 720 q^{81} + 512 q^{82} - 1952 q^{83} - 600 q^{84} + 128 q^{85} - 388 q^{87} + 96 q^{88} + 1500 q^{89} - 640 q^{90} + 288 q^{92} + 372 q^{93} + 668 q^{95} + 448 q^{97} + 224 q^{98} + O(q^{100}) \)

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.w.a 350.w 175.w $320$ $9.537$ None \(-40\) \(0\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{60}]$
350.3.w.b 350.w 175.w $320$ $9.537$ None \(40\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{60}]$

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

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