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Properties

Label 350.2.m
Level $350$
Weight $2$
Character orbit 350.m
Rep. character $\chi_{350}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $64$
Newform subspaces $2$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(350, [\chi])\).

Total New Old
Modular forms 256 64 192
Cusp forms 224 64 160
Eisenstein series 32 0 32

Trace form

\( 64 q + 16 q^{4} + 16 q^{5} + 28 q^{9} + O(q^{10}) \) \( 64 q + 16 q^{4} + 16 q^{5} + 28 q^{9} - 4 q^{10} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 8 q^{15} - 16 q^{16} - 24 q^{19} + 4 q^{20} - 4 q^{21} - 20 q^{22} - 20 q^{23} - 20 q^{25} + 8 q^{26} - 60 q^{27} - 8 q^{29} - 32 q^{30} - 24 q^{31} - 40 q^{33} - 4 q^{35} - 28 q^{36} + 20 q^{37} - 12 q^{39} + 4 q^{40} + 8 q^{41} + 4 q^{44} + 72 q^{45} + 4 q^{46} + 60 q^{47} + 20 q^{48} - 64 q^{49} + 4 q^{50} - 8 q^{51} + 20 q^{53} + 24 q^{54} + 44 q^{55} - 4 q^{56} + 12 q^{59} - 8 q^{60} + 48 q^{61} - 20 q^{63} + 16 q^{64} - 96 q^{65} - 20 q^{67} + 84 q^{69} + 4 q^{70} + 48 q^{71} - 80 q^{73} - 88 q^{74} - 16 q^{76} + 40 q^{77} - 40 q^{78} - 40 q^{79} - 4 q^{80} + 56 q^{81} + 60 q^{83} + 4 q^{84} - 92 q^{85} - 20 q^{86} - 40 q^{87} - 4 q^{89} + 12 q^{90} - 4 q^{91} + 4 q^{95} + 60 q^{97} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
350.2.m.a 350.m 25.e $24$ $2.795$ None \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{10}]$
350.2.m.b 350.m 25.e $40$ $2.795$ None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)