Properties

Label 510.2.c
Level $510$
Weight $2$
Character orbit 510.c
Rep. character $\chi_{510}(271,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $4$
Sturm bound $216$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 510.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(216\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 116 12 104
Cusp forms 100 12 88
Eisenstein series 16 0 16

Trace form

\( 12 q + 12 q^{4} - 12 q^{9} + 24 q^{13} + 12 q^{16} + 8 q^{17} + 16 q^{19} - 12 q^{25} + 4 q^{30} - 8 q^{33} + 12 q^{34} - 16 q^{35} - 12 q^{36} - 16 q^{38} + 8 q^{42} + 24 q^{43} - 16 q^{47} - 28 q^{49}+ \cdots - 16 q^{94}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
510.2.c.a 510.c 17.b $2$ $4.072$ \(\Q(\sqrt{-1}) \) None 510.2.c.a \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+i q^{3}+q^{4}-i q^{5}-i q^{6}+\cdots\)
510.2.c.b 510.c 17.b $2$ $4.072$ \(\Q(\sqrt{-1}) \) None 510.2.c.b \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+i q^{3}+q^{4}+i q^{5}+i q^{6}+\cdots\)
510.2.c.c 510.c 17.b $4$ $4.072$ \(\Q(i, \sqrt{13})\) None 510.2.c.c \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{1}q^{6}+\cdots\)
510.2.c.d 510.c 17.b $4$ $4.072$ \(\Q(\zeta_{8})\) None 510.2.c.d \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta_1 q^{3}+q^{4}-\beta_1 q^{5}+\beta_1 q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(510, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)