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
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

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

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

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database