Properties

Label 735.2.p
Level $735$
Weight $2$
Character orbit 735.p
Rep. character $\chi_{735}(374,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
Newform subspaces $7$
Sturm bound $224$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 7 \)
Sturm bound: \(224\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(13\), \(257\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(735, [\chi])\).

Total New Old
Modular forms 256 176 80
Cusp forms 192 144 48
Eisenstein series 64 32 32

Trace form

\( 144 q - 60 q^{4} + 8 q^{9} + O(q^{10}) \) \( 144 q - 60 q^{4} + 8 q^{9} + 20 q^{15} - 36 q^{16} - 18 q^{24} + 16 q^{25} - 14 q^{30} - 164 q^{36} + 26 q^{39} + 72 q^{40} + 18 q^{45} + 20 q^{46} - 14 q^{51} + 36 q^{54} - 32 q^{60} - 36 q^{61} - 120 q^{64} + 72 q^{66} - 72 q^{75} - 60 q^{79} - 20 q^{81} - 104 q^{85} + 72 q^{94} + 90 q^{96} + 44 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(735, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
735.2.p.a 735.p 105.p $8$ $5.869$ \(\Q(\zeta_{24})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{2}q^{2}+(-1+\zeta_{24}+\zeta_{24}^{5})q^{3}+\cdots\)
735.2.p.b 735.p 105.p $8$ $5.869$ 8.0.\(\cdots\).2 \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{6}q^{3}+(2+2\beta _{4})q^{4}+(\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots\)
735.2.p.c 735.p 105.p $8$ $5.869$ \(\Q(\zeta_{24})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{2}q^{2}+(1-\zeta_{24}+\zeta_{24}^{5})q^{3}+\cdots\)
735.2.p.d 735.p 105.p $16$ $5.869$ 16.0.\(\cdots\).5 \(\Q(\sqrt{-15}) \) \(0\) \(-24\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(-\beta _{2}+\beta _{7})q^{2}+(-1+\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
735.2.p.e 735.p 105.p $16$ $5.869$ 16.0.\(\cdots\).5 \(\Q(\sqrt{-15}) \) \(0\) \(24\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(-\beta _{2}+\beta _{7})q^{2}+(1-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
735.2.p.f 735.p 105.p $24$ $5.869$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
735.2.p.g 735.p 105.p $64$ $5.869$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(735, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)