Properties

Label 671.2.bn
Level $671$
Weight $2$
Character orbit 671.bn
Rep. character $\chi_{671}(12,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $416$
Newform subspaces $2$
Sturm bound $124$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 671 = 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 671.bn (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 61 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 2 \)
Sturm bound: \(124\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(671, [\chi])\).

Total New Old
Modular forms 512 416 96
Cusp forms 480 416 64
Eisenstein series 32 0 32

Trace form

\( 416 q + 2 q^{2} - 4 q^{3} + 60 q^{4} - 20 q^{5} - 16 q^{6} - 18 q^{7} - 12 q^{8} - 120 q^{9} + O(q^{10}) \) \( 416 q + 2 q^{2} - 4 q^{3} + 60 q^{4} - 20 q^{5} - 16 q^{6} - 18 q^{7} - 12 q^{8} - 120 q^{9} - 48 q^{10} + 94 q^{12} + 8 q^{13} - 34 q^{14} - 16 q^{15} + 36 q^{16} + 16 q^{17} + 22 q^{18} - 44 q^{19} - 4 q^{20} - 8 q^{21} + 2 q^{22} + 28 q^{23} - 74 q^{24} - 20 q^{25} - 20 q^{26} - 16 q^{27} - 40 q^{28} - 20 q^{29} - 52 q^{30} + 2 q^{31} - 66 q^{32} - 116 q^{34} - 8 q^{35} - 124 q^{36} + 32 q^{37} + 30 q^{38} + 4 q^{39} + 30 q^{40} + 16 q^{41} + 8 q^{42} - 36 q^{43} - 50 q^{45} + 140 q^{46} - 84 q^{47} - 52 q^{48} + 56 q^{49} + 52 q^{50} - 40 q^{51} + 208 q^{52} - 44 q^{53} + 168 q^{54} + 120 q^{56} + 20 q^{57} - 118 q^{58} + 6 q^{59} - 120 q^{60} + 24 q^{61} - 52 q^{62} + 54 q^{63} - 116 q^{64} - 150 q^{65} + 8 q^{66} - 30 q^{67} + 34 q^{68} + 80 q^{69} - 54 q^{70} - 8 q^{71} + 248 q^{72} + 30 q^{73} + 104 q^{74} - 58 q^{75} - 176 q^{76} + 2 q^{77} - 28 q^{78} + 88 q^{79} - 82 q^{80} - 220 q^{81} - 128 q^{82} - 10 q^{83} - 56 q^{84} + 20 q^{85} - 106 q^{86} + 18 q^{87} - 48 q^{88} - 20 q^{89} - 10 q^{90} - 16 q^{91} - 82 q^{92} - 24 q^{93} + 152 q^{94} - 114 q^{95} + 188 q^{96} - 42 q^{97} - 146 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(671, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
671.2.bn.a 671.bn 61.i $208$ $5.358$ None \(0\) \(-2\) \(-10\) \(-10\) $\mathrm{SU}(2)[C_{15}]$
671.2.bn.b 671.bn 61.i $208$ $5.358$ None \(2\) \(-2\) \(-10\) \(-8\) $\mathrm{SU}(2)[C_{15}]$

Decomposition of \(S_{2}^{\mathrm{old}}(671, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(671, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(61, [\chi])\)\(^{\oplus 2}\)