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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
245.2.q.a \(96\) \(1.956\) None \(-1\) \(1\) \(-8\) \(0\)
245.2.q.b \(120\) \(1.956\) None \(1\) \(1\) \(10\) \(-2\)

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

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