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Properties

Label 465.2.bp
Level $465$
Weight $2$
Character orbit 465.bp
Rep. character $\chi_{465}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $256$
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.bp (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{30})\)
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 544 256 288
Cusp forms 480 256 224
Eisenstein series 64 0 64

Trace form

\( 256 q + 60 q^{4} + 14 q^{6} - 32 q^{9} + O(q^{10}) \) \( 256 q + 60 q^{4} + 14 q^{6} - 32 q^{9} - 2 q^{10} - 4 q^{14} - 8 q^{15} - 56 q^{16} + 28 q^{19} - 36 q^{20} - 32 q^{21} - 28 q^{24} - 24 q^{25} + 36 q^{26} - 8 q^{29} + 8 q^{30} - 12 q^{31} + 26 q^{34} - 12 q^{35} - 130 q^{36} - 8 q^{39} + 34 q^{40} - 12 q^{41} + 104 q^{44} + 2 q^{46} - 88 q^{49} - 2 q^{50} - 4 q^{51} - 2 q^{54} + 84 q^{55} - 24 q^{56} - 76 q^{59} + 24 q^{60} - 168 q^{61} + 32 q^{64} + 130 q^{65} - 12 q^{66} + 24 q^{69} + 146 q^{70} - 248 q^{71} - 132 q^{74} + 12 q^{75} - 304 q^{76} + 108 q^{79} - 16 q^{80} + 32 q^{81} + 40 q^{84} - 12 q^{85} + 128 q^{86} - 52 q^{89} + 2 q^{90} + 32 q^{91} + 216 q^{94} - 118 q^{95} - 70 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
465.2.bp.a 465.bp 155.u $256$ $3.713$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$

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

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