Properties

Label 465.2.ba
Level $465$
Weight $2$
Character orbit 465.ba
Rep. character $\chi_{465}(4,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $128$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 465.ba (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(465, [\chi])\).

Total New Old
Modular forms 272 128 144
Cusp forms 240 128 112
Eisenstein series 32 0 32

Trace form

\( 128q + 36q^{4} - 20q^{6} + 32q^{9} + O(q^{10}) \) \( 128q + 36q^{4} - 20q^{6} + 32q^{9} + 2q^{10} + 4q^{14} - 4q^{15} - 40q^{16} - 4q^{19} + 36q^{20} + 20q^{21} - 20q^{24} + 12q^{25} + 24q^{26} - 28q^{29} - 8q^{30} - 12q^{31} - 44q^{34} + 124q^{36} - 4q^{39} - 22q^{40} + 36q^{41} - 80q^{44} + 46q^{46} + 64q^{49} + 68q^{50} - 8q^{51} - 10q^{54} + 12q^{55} - 432q^{56} + 88q^{59} + 12q^{60} - 120q^{61} + 40q^{64} - 4q^{65} + 12q^{66} - 24q^{69} - 74q^{70} + 44q^{71} + 132q^{74} - 12q^{75} - 14q^{76} - 132q^{79} + 70q^{80} - 32q^{81} + 8q^{84} + 48q^{85} - 104q^{86} + 52q^{89} - 2q^{90} - 32q^{91} - 204q^{94} + 34q^{95} - 20q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(465, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
465.2.ba.a \(128\) \(3.713\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(465, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(465, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)