Properties

Label 465.2.c
Level $465$
Weight $2$
Character orbit 465.c
Rep. character $\chi_{465}(94,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $2$
Sturm bound $128$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 68 32 36
Cusp forms 60 32 28
Eisenstein series 8 0 8

Trace form

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

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.c.a 465.c 5.b $10$ $3.713$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}+\beta _{8})q^{2}+\beta _{3}q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
465.2.c.b 465.c 5.b $22$ $3.713$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

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