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Properties

Label 245.2.k
Level $245$
Weight $2$
Character orbit 245.k
Rep. character $\chi_{245}(36,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $120$
Newform subspaces $2$
Sturm bound $56$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.k (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(245, [\chi])\).

Total New Old
Modular forms 180 120 60
Cusp forms 156 120 36
Eisenstein series 24 0 24

Trace form

\( 120 q - 4 q^{3} - 24 q^{4} - 2 q^{5} + 10 q^{6} - 6 q^{7} - 14 q^{9} + O(q^{10}) \) \( 120 q - 4 q^{3} - 24 q^{4} - 2 q^{5} + 10 q^{6} - 6 q^{7} - 14 q^{9} - 2 q^{10} - 4 q^{11} + 38 q^{12} - 24 q^{13} + 48 q^{14} - 40 q^{16} - 16 q^{17} - 36 q^{18} - 16 q^{19} - 14 q^{20} - 30 q^{21} - 32 q^{22} + 30 q^{23} + 28 q^{24} - 20 q^{25} - 34 q^{26} + 14 q^{27} + 42 q^{28} + 18 q^{29} - 4 q^{30} - 28 q^{31} - 40 q^{32} - 36 q^{33} - 20 q^{34} + 10 q^{35} - 50 q^{36} + 54 q^{37} - 52 q^{38} + 16 q^{39} - 6 q^{40} - 18 q^{41} + 48 q^{42} - 32 q^{43} + 6 q^{44} - 18 q^{45} + 6 q^{46} + 60 q^{47} + 44 q^{48} - 24 q^{49} - 32 q^{51} + 104 q^{52} - 20 q^{53} - 90 q^{54} - 16 q^{55} + 68 q^{56} - 60 q^{57} + 12 q^{58} - 24 q^{59} + 70 q^{60} + 36 q^{61} - 68 q^{62} + 68 q^{63} - 56 q^{64} - 12 q^{65} + 98 q^{66} - 40 q^{67} + 52 q^{68} + 60 q^{69} - 22 q^{70} - 8 q^{71} - 132 q^{72} - 26 q^{73} - 58 q^{74} - 4 q^{75} - 104 q^{76} - 38 q^{77} + 44 q^{78} - 40 q^{79} + 68 q^{80} + 62 q^{81} - 38 q^{82} - 62 q^{83} - 34 q^{84} - 4 q^{85} - 8 q^{86} - 36 q^{87} - 50 q^{88} + 14 q^{89} - 46 q^{90} + 196 q^{91} + 2 q^{92} - 100 q^{93} + 192 q^{94} - 8 q^{95} + 284 q^{96} - 32 q^{97} - 90 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.2.k.a 245.k 49.e $54$ $1.956$ None \(1\) \(-2\) \(9\) \(-1\) $\mathrm{SU}(2)[C_{7}]$
245.2.k.b 245.k 49.e $66$ $1.956$ None \(-1\) \(-2\) \(-11\) \(-5\) $\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{2}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(245, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)