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Properties

Label 735.2.v
Level $735$
Weight $2$
Character orbit 735.v
Rep. character $\chi_{735}(178,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $160$
Newform subspaces $4$
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.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(224\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

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

Total New Old
Modular forms 512 160 352
Cusp forms 384 160 224
Eisenstein series 128 0 128

Trace form

\( 160 q + 12 q^{5} + 24 q^{8} + O(q^{10}) \) \( 160 q + 12 q^{5} + 24 q^{8} + 12 q^{10} + 8 q^{11} + 8 q^{15} + 96 q^{16} + 24 q^{22} - 20 q^{25} - 24 q^{26} - 16 q^{30} - 24 q^{31} - 24 q^{32} + 36 q^{33} - 160 q^{36} + 4 q^{37} - 12 q^{38} - 12 q^{40} - 56 q^{43} + 88 q^{46} + 60 q^{47} - 72 q^{50} + 8 q^{51} + 108 q^{52} - 64 q^{53} - 32 q^{57} - 108 q^{58} - 20 q^{60} + 24 q^{61} + 20 q^{65} - 72 q^{66} - 24 q^{67} - 132 q^{68} - 16 q^{71} - 12 q^{72} - 36 q^{73} - 48 q^{75} - 128 q^{78} + 12 q^{80} + 80 q^{81} - 12 q^{82} + 88 q^{85} + 48 q^{86} + 24 q^{87} + 32 q^{88} + 120 q^{92} + 48 q^{93} - 4 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.v.a 735.v 35.k $32$ $5.869$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
735.2.v.b 735.v 35.k $32$ $5.869$ None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{12}]$
735.2.v.c 735.v 35.k $48$ $5.869$ None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{12}]$
735.2.v.d 735.v 35.k $48$ $5.869$ None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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