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Properties

Label 605.2.k
Level $605$
Weight $2$
Character orbit 605.k
Rep. character $\chi_{605}(56,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $440$
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.k (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{11})\)
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 680 440 240
Cusp forms 640 440 200
Eisenstein series 40 0 40

Trace form

\( 440 q - 6 q^{2} - 4 q^{3} - 48 q^{4} - 4 q^{6} - 4 q^{7} - 18 q^{8} + 424 q^{9} + O(q^{10}) \) \( 440 q - 6 q^{2} - 4 q^{3} - 48 q^{4} - 4 q^{6} - 4 q^{7} - 18 q^{8} + 424 q^{9} - 2 q^{10} - 12 q^{11} + 54 q^{12} + 14 q^{13} + 28 q^{14} + 18 q^{15} - 72 q^{16} - 32 q^{17} - 46 q^{18} - 16 q^{19} - 32 q^{21} - 34 q^{22} + 20 q^{23} + 36 q^{24} - 44 q^{25} - 36 q^{26} - 40 q^{27} - 52 q^{28} - 40 q^{29} - 20 q^{30} + 24 q^{31} - 62 q^{32} - 44 q^{33} - 64 q^{34} - 12 q^{35} - 124 q^{36} - 24 q^{37} - 32 q^{38} - 40 q^{39} + 60 q^{40} - 56 q^{41} - 84 q^{42} - 36 q^{43} - 58 q^{44} - 68 q^{46} - 28 q^{47} - 104 q^{48} - 28 q^{49} - 6 q^{50} + 54 q^{51} + 204 q^{52} + 160 q^{53} + 50 q^{54} - 8 q^{55} - 54 q^{56} + 74 q^{57} + 126 q^{58} - 44 q^{59} - 44 q^{60} - 56 q^{61} + 22 q^{62} - 84 q^{63} + 68 q^{64} - 24 q^{65} - 102 q^{66} - 34 q^{67} - 144 q^{68} - 104 q^{69} - 24 q^{70} - 68 q^{71} - 234 q^{72} - 36 q^{73} - 92 q^{74} - 4 q^{75} + 120 q^{76} + 180 q^{77} + 72 q^{78} + 36 q^{79} - 16 q^{80} + 328 q^{81} - 44 q^{82} - 68 q^{83} - 256 q^{84} + 50 q^{85} - 100 q^{86} - 152 q^{87} + 68 q^{88} + 8 q^{89} + 62 q^{90} + 28 q^{91} + 148 q^{92} - 30 q^{93} - 52 q^{94} - 16 q^{95} + 20 q^{96} - 2 q^{97} + 194 q^{98} - 156 q^{99} + O(q^{100}) \)

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.k.a 605.k 121.e $220$ $4.831$ None \(-4\) \(-4\) \(-22\) \(-8\) $\mathrm{SU}(2)[C_{11}]$
605.2.k.b 605.k 121.e $220$ $4.831$ None \(-2\) \(0\) \(22\) \(4\) $\mathrm{SU}(2)[C_{11}]$

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

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