Properties

Label 350.2.m
Level 350
Weight 2
Character orbit m
Rep. character \(\chi_{350}(29,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 64
Newforms 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: \(\Q(\zeta_{10})\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(350, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
350.2.m.a \(24\) \(2.795\) None \(0\) \(0\) \(10\) \(0\)
350.2.m.b \(40\) \(2.795\) None \(0\) \(0\) \(6\) \(0\)

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

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