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Properties

Label 510.2.bf
Level $510$
Weight $2$
Character orbit 510.bf
Rep. character $\chi_{510}(11,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $192$
Newform subspaces $2$
Sturm bound $216$
Trace bound $12$

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Defining parameters

Level: \( N \) \(=\) \( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 510.bf (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 51 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(12\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(510, [\chi])\).

Total New Old
Modular forms 928 192 736
Cusp forms 800 192 608
Eisenstein series 128 0 128

Trace form

\( 192 q + O(q^{10}) \) \( 192 q + 16 q^{12} + 64 q^{18} + 16 q^{24} + 32 q^{31} + 64 q^{37} - 32 q^{39} + 32 q^{43} - 64 q^{45} - 64 q^{46} - 64 q^{49} - 128 q^{51} - 16 q^{54} - 64 q^{55} + 16 q^{57} - 64 q^{58} - 32 q^{60} - 64 q^{61} - 96 q^{63} - 16 q^{66} + 64 q^{69} + 16 q^{81} - 96 q^{87} + 192 q^{91} - 128 q^{93} - 64 q^{97} - 112 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(510, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
510.2.bf.a 510.bf 51.i $96$ $4.072$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
510.2.bf.b 510.bf 51.i $96$ $4.072$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(510, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(510, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)