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Properties

Label 465.2.bm
Level $465$
Weight $2$
Character orbit 465.bm
Rep. character $\chi_{465}(44,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $480$
Newform subspaces $5$
Sturm bound $128$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 465.bm (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 5 \)
Sturm bound: \(128\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 544 544 0
Cusp forms 480 480 0
Eisenstein series 64 64 0

Trace form

\( 480 q - 140 q^{4} - 12 q^{6} - 22 q^{9} + O(q^{10}) \) \( 480 q - 140 q^{4} - 12 q^{6} - 22 q^{9} + 10 q^{10} - 80 q^{16} - 56 q^{19} - 14 q^{21} - 18 q^{25} - 64 q^{31} - 26 q^{34} - 32 q^{36} - 32 q^{39} + 36 q^{40} + 39 q^{45} - 90 q^{46} - 4 q^{49} - 128 q^{51} - 20 q^{54} - 82 q^{55} + 175 q^{60} - 224 q^{66} - 60 q^{69} - 14 q^{70} + 16 q^{75} + 104 q^{76} - 112 q^{79} - 26 q^{81} + 152 q^{84} + 50 q^{85} + 49 q^{90} - 20 q^{91} - 224 q^{94} - 66 q^{96} - 156 q^{99} + O(q^{100}) \)

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.bm.a 465.bm 465.am $8$ $3.713$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-15}) \) \(-3\) \(3\) \(0\) \(0\) $\mathrm{U}(1)[D_{30}]$ \(q+(-1-\zeta_{15}-\zeta_{15}^{5}-\zeta_{15}^{6})q^{2}+\cdots\)
465.2.bm.b 465.bm 465.am $8$ $3.713$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-15}) \) \(-3\) \(3\) \(0\) \(0\) $\mathrm{U}(1)[D_{30}]$ \(q+(\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
465.2.bm.c 465.bm 465.am $8$ $3.713$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-15}) \) \(3\) \(-3\) \(0\) \(0\) $\mathrm{U}(1)[D_{30}]$ \(q+(1+\zeta_{15}+\zeta_{15}^{5}+\zeta_{15}^{6})q^{2}+(-\zeta_{15}^{2}+\cdots)q^{3}+\cdots\)
465.2.bm.d 465.bm 465.am $8$ $3.713$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-15}) \) \(3\) \(-3\) \(0\) \(0\) $\mathrm{U}(1)[D_{30}]$ \(q+(-\zeta_{15}+\zeta_{15}^{2}+\zeta_{15}^{3}+\zeta_{15}^{4}+\cdots)q^{2}+\cdots\)
465.2.bm.e 465.bm 465.am $448$ $3.713$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$