Properties

Label 735.2.d
Level $735$
Weight $2$
Character orbit 735.d
Rep. character $\chi_{735}(589,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $6$
Sturm bound $224$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(224\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(19\)

Dimensions

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

Total New Old
Modular forms 128 40 88
Cusp forms 96 40 56
Eisenstein series 32 0 32

Trace form

\( 40 q - 40 q^{4} - 4 q^{5} + 4 q^{6} - 40 q^{9} + O(q^{10}) \) \( 40 q - 40 q^{4} - 4 q^{5} + 4 q^{6} - 40 q^{9} + 8 q^{10} - 4 q^{15} + 24 q^{16} + 28 q^{20} - 12 q^{24} + 8 q^{25} - 24 q^{26} - 8 q^{29} + 8 q^{30} + 16 q^{31} - 32 q^{34} + 40 q^{36} + 8 q^{39} - 16 q^{40} - 8 q^{41} + 56 q^{44} + 4 q^{45} - 32 q^{50} - 8 q^{51} - 4 q^{54} + 8 q^{55} + 16 q^{59} + 16 q^{60} + 16 q^{61} - 8 q^{64} - 68 q^{65} - 8 q^{66} - 8 q^{69} - 24 q^{71} + 32 q^{74} - 16 q^{75} - 16 q^{76} + 32 q^{79} - 44 q^{80} + 40 q^{81} - 56 q^{85} - 32 q^{86} + 40 q^{89} - 8 q^{90} - 32 q^{94} - 36 q^{95} + 68 q^{96} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
735.2.d.a $2$ $5.869$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}-iq^{3}+q^{4}+(-1+2i)q^{5}+\cdots\)
735.2.d.b $6$ $5.869$ 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(-1+\beta _{3}+\beta _{5})q^{4}+\cdots\)
735.2.d.c $8$ $5.869$ 8.0.309760000.3 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-2+\beta _{6}-\beta _{7})q^{4}+\cdots\)
735.2.d.d $8$ $5.869$ 8.0.2058981376.2 None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{6}q^{2}-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
735.2.d.e $8$ $5.869$ 8.0.2058981376.2 None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
735.2.d.f $8$ $5.869$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{4}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{3}q^{4}+(-\zeta_{24}^{2}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)