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Properties

Label 605.2.s
Level $605$
Weight $2$
Character orbit 605.s
Rep. character $\chi_{605}(16,\cdot)$
Character field $\Q(\zeta_{55})$
Dimension $1760$
Newform subspaces $2$
Sturm bound $132$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.s (of order \(55\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{55})\)
Newform subspaces: \( 2 \)
Sturm bound: \(132\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(605, [\chi])\).

Total New Old
Modular forms 2720 1760 960
Cusp forms 2560 1760 800
Eisenstein series 160 0 160

Trace form

\( 1760 q + 6 q^{2} + 4 q^{3} + 48 q^{4} - 6 q^{6} + 4 q^{7} - 2 q^{8} - 434 q^{9} + O(q^{10}) \) \( 1760 q + 6 q^{2} + 4 q^{3} + 48 q^{4} - 6 q^{6} + 4 q^{7} - 2 q^{8} - 434 q^{9} - 8 q^{10} + 2 q^{11} - 54 q^{12} - 24 q^{13} - 48 q^{14} - 28 q^{15} + 52 q^{16} + 12 q^{17} - 14 q^{18} - 14 q^{19} + 32 q^{21} - 26 q^{22} - 20 q^{23} - 126 q^{24} + 44 q^{25} - 4 q^{26} - 20 q^{27} + 2 q^{28} - 10 q^{29} + 20 q^{30} - 44 q^{31} - 28 q^{32} + 14 q^{33} + 64 q^{34} + 12 q^{35} + 14 q^{36} - 36 q^{37} - 18 q^{38} - 30 q^{39} - 60 q^{40} - 4 q^{41} - 66 q^{42} - 4 q^{43} + 18 q^{44} + 38 q^{46} - 12 q^{47} - 6 q^{48} - 2 q^{49} + 6 q^{50} - 124 q^{51} - 254 q^{52} - 240 q^{53} - 130 q^{54} - 12 q^{55} + 54 q^{56} - 104 q^{57} - 216 q^{58} + 34 q^{59} - 26 q^{60} - 4 q^{61} - 42 q^{62} - 26 q^{63} - 168 q^{64} - 16 q^{65} - 48 q^{66} + 34 q^{67} - 46 q^{68} + 14 q^{69} - 36 q^{70} - 32 q^{71} + 64 q^{72} - 34 q^{73} - 68 q^{74} - 6 q^{75} - 280 q^{76} - 270 q^{77} - 72 q^{78} - 186 q^{79} - 24 q^{80} - 468 q^{81} - 126 q^{82} - 2 q^{83} - 24 q^{84} - 50 q^{85} + 10 q^{86} - 68 q^{87} - 228 q^{88} - 8 q^{89} - 62 q^{90} - 188 q^{91} - 388 q^{92} - 50 q^{93} - 138 q^{94} + 16 q^{95} - 270 q^{96} - 138 q^{97} - 284 q^{98} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(605, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
605.2.s.a 605.s 121.g $880$ $4.831$ None \(2\) \(5\) \(-22\) \(1\) $\mathrm{SU}(2)[C_{55}]$
605.2.s.b 605.s 121.g $880$ $4.831$ None \(4\) \(-1\) \(22\) \(3\) $\mathrm{SU}(2)[C_{55}]$

Decomposition of \(S_{2}^{\mathrm{old}}(605, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(605, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)