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Properties

Label 805.2.u
Level $805$
Weight $2$
Character orbit 805.u
Rep. character $\chi_{805}(36,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $480$
Newform subspaces $4$
Sturm bound $192$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.u (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(805, [\chi])\).

Total New Old
Modular forms 1000 480 520
Cusp forms 920 480 440
Eisenstein series 80 0 80

Trace form

\( 480 q + 4 q^{2} - 36 q^{4} + 20 q^{6} + 4 q^{7} + 24 q^{8} - 48 q^{9} + O(q^{10}) \) \( 480 q + 4 q^{2} - 36 q^{4} + 20 q^{6} + 4 q^{7} + 24 q^{8} - 48 q^{9} + 8 q^{10} + 16 q^{11} + 12 q^{12} + 8 q^{13} + 4 q^{14} + 8 q^{15} - 40 q^{16} - 28 q^{17} + 32 q^{18} - 20 q^{19} - 56 q^{22} + 20 q^{23} - 216 q^{24} - 48 q^{25} - 60 q^{26} + 48 q^{27} + 28 q^{28} + 4 q^{29} + 8 q^{30} + 12 q^{31} + 8 q^{32} + 24 q^{33} + 12 q^{34} - 94 q^{36} + 32 q^{37} + 32 q^{38} - 8 q^{39} - 128 q^{40} - 48 q^{41} + 8 q^{42} - 48 q^{43} + 34 q^{44} + 16 q^{45} - 264 q^{46} + 80 q^{47} - 252 q^{48} - 48 q^{49} - 18 q^{50} - 24 q^{51} + 132 q^{52} - 8 q^{53} - 60 q^{54} - 72 q^{55} + 12 q^{56} - 28 q^{57} + 78 q^{58} - 20 q^{60} + 72 q^{61} - 140 q^{62} + 36 q^{63} + 24 q^{65} + 72 q^{66} + 8 q^{67} + 216 q^{68} + 84 q^{69} + 80 q^{71} + 280 q^{72} - 16 q^{73} - 22 q^{74} + 24 q^{76} - 72 q^{77} - 28 q^{78} - 48 q^{79} + 32 q^{80} - 72 q^{81} - 148 q^{82} - 244 q^{83} - 252 q^{84} + 32 q^{85} + 176 q^{86} + 40 q^{87} + 138 q^{88} - 152 q^{89} + 64 q^{90} + 16 q^{91} + 120 q^{92} - 432 q^{93} + 100 q^{94} + 16 q^{95} + 132 q^{96} - 160 q^{97} - 18 q^{98} + 104 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(805, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
805.2.u.a 805.u 23.c $110$ $6.428$ None \(0\) \(-2\) \(11\) \(-11\) $\mathrm{SU}(2)[C_{11}]$
805.2.u.b 805.u 23.c $110$ $6.428$ None \(4\) \(2\) \(-11\) \(-11\) $\mathrm{SU}(2)[C_{11}]$
805.2.u.c 805.u 23.c $130$ $6.428$ None \(-2\) \(-2\) \(13\) \(13\) $\mathrm{SU}(2)[C_{11}]$
805.2.u.d 805.u 23.c $130$ $6.428$ None \(2\) \(2\) \(-13\) \(13\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(805, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)