Properties

Label 245.2.q
Level $245$
Weight $2$
Character orbit 245.q
Rep. character $\chi_{245}(11,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $216$
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.q (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
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 360 216 144
Cusp forms 312 216 96
Eisenstein series 48 0 48

Trace form

\( 216 q + 2 q^{3} + 16 q^{4} + 2 q^{5} - 10 q^{6} - 2 q^{7} + O(q^{10}) \) \( 216 q + 2 q^{3} + 16 q^{4} + 2 q^{5} - 10 q^{6} - 2 q^{7} + 2 q^{10} - 2 q^{11} - 76 q^{12} + 8 q^{13} - 66 q^{14} + 8 q^{16} + 4 q^{17} - 18 q^{18} - 4 q^{20} - 14 q^{21} + 32 q^{22} - 48 q^{23} - 82 q^{24} + 18 q^{25} - 26 q^{26} - 46 q^{27} - 62 q^{28} - 18 q^{29} - 2 q^{30} - 12 q^{31} - 20 q^{32} + 12 q^{33} - 52 q^{34} - 10 q^{35} - 6 q^{36} - 50 q^{37} + 64 q^{38} - 48 q^{39} + 6 q^{40} + 48 q^{41} + 30 q^{42} + 4 q^{43} + 24 q^{44} + 66 q^{46} - 24 q^{47} + 100 q^{48} + 46 q^{49} + 26 q^{51} + 92 q^{52} + 32 q^{53} + 90 q^{54} - 8 q^{55} - 74 q^{56} + 32 q^{57} + 90 q^{58} + 6 q^{59} - 112 q^{60} - 104 q^{61} + 80 q^{62} - 98 q^{63} - 6 q^{65} - 242 q^{66} - 6 q^{67} - 148 q^{68} - 156 q^{69} + 10 q^{70} + 8 q^{71} - 66 q^{72} - 38 q^{73} - 50 q^{74} + 2 q^{75} - 32 q^{76} - 70 q^{77} - 44 q^{78} - 6 q^{79} - 92 q^{80} - 4 q^{81} + 122 q^{82} - 46 q^{83} + 296 q^{84} + 4 q^{85} + 164 q^{86} + 222 q^{87} - 130 q^{88} + 64 q^{89} + 16 q^{90} - 98 q^{91} - 44 q^{92} - 36 q^{93} + 18 q^{94} - 4 q^{95} + 172 q^{96} + 88 q^{97} - 42 q^{98} - 8 q^{99} + O(q^{100}) \)

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.q.a 245.q 49.g $96$ $1.956$ None \(-1\) \(1\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{21}]$
245.2.q.b 245.q 49.g $120$ $1.956$ None \(1\) \(1\) \(10\) \(-2\) $\mathrm{SU}(2)[C_{21}]$

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

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