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Properties

Label 435.2.u
Level $435$
Weight $2$
Character orbit 435.u
Rep. character $\chi_{435}(16,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $120$
Newform subspaces $4$
Sturm bound $120$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 435 = 3 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 435.u (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(435, [\chi])\).

Total New Old
Modular forms 384 120 264
Cusp forms 336 120 216
Eisenstein series 48 0 48

Trace form

\( 120 q + 8 q^{2} - 12 q^{4} + 8 q^{7} + 24 q^{8} - 20 q^{9} + O(q^{10}) \) \( 120 q + 8 q^{2} - 12 q^{4} + 8 q^{7} + 24 q^{8} - 20 q^{9} - 40 q^{11} + 8 q^{13} + 24 q^{14} - 52 q^{16} + 24 q^{17} + 8 q^{18} + 8 q^{19} - 32 q^{22} + 12 q^{23} + 12 q^{24} - 20 q^{25} + 56 q^{26} - 120 q^{28} + 4 q^{29} - 24 q^{30} + 12 q^{31} - 156 q^{32} + 16 q^{33} + 36 q^{34} + 8 q^{35} - 12 q^{36} + 36 q^{37} + 16 q^{38} + 8 q^{39} + 8 q^{41} + 36 q^{42} + 40 q^{43} + 20 q^{44} + 56 q^{46} - 72 q^{47} + 32 q^{48} - 20 q^{49} + 8 q^{50} - 60 q^{51} - 44 q^{52} + 96 q^{53} - 20 q^{55} - 56 q^{56} - 48 q^{57} + 28 q^{58} - 16 q^{59} + 16 q^{61} - 116 q^{62} + 8 q^{63} + 16 q^{64} - 116 q^{66} - 32 q^{67} + 8 q^{68} - 32 q^{69} + 24 q^{70} - 44 q^{71} - 4 q^{72} + 36 q^{73} + 28 q^{74} + 76 q^{76} + 80 q^{77} + 76 q^{78} - 36 q^{79} + 32 q^{80} - 20 q^{81} - 108 q^{82} - 16 q^{83} + 24 q^{84} + 8 q^{85} + 208 q^{86} + 16 q^{87} - 64 q^{88} + 60 q^{89} + 112 q^{91} + 44 q^{92} + 24 q^{93} + 76 q^{94} + 16 q^{95} - 76 q^{96} + 60 q^{97} + 52 q^{98} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(435, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
435.2.u.a 435.u 29.d $30$ $3.473$ None 435.2.u.a \(1\) \(-5\) \(5\) \(0\) $\mathrm{SU}(2)[C_{7}]$
435.2.u.b 435.u 29.d $30$ $3.473$ None 435.2.u.b \(1\) \(5\) \(-5\) \(4\) $\mathrm{SU}(2)[C_{7}]$
435.2.u.c 435.u 29.d $30$ $3.473$ None 435.2.u.c \(3\) \(-5\) \(-5\) \(4\) $\mathrm{SU}(2)[C_{7}]$
435.2.u.d 435.u 29.d $30$ $3.473$ None 435.2.u.d \(3\) \(5\) \(5\) \(0\) $\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{2}^{\mathrm{old}}(435, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(435, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)