Properties

Label 245.2.a
Level $245$
Weight $2$
Character orbit 245.a
Rep. character $\chi_{245}(1,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $8$
Sturm bound $56$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(56\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(245))\).

Total New Old
Modular forms 36 13 23
Cusp forms 21 13 8
Eisenstein series 15 0 15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(9\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(245))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 7
245.2.a.a \(1\) \(1.956\) \(\Q\) None \(-2\) \(-3\) \(1\) \(0\) \(-\) \(-\) \(q-2q^{2}-3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots\)
245.2.a.b \(1\) \(1.956\) \(\Q\) None \(-2\) \(3\) \(-1\) \(0\) \(+\) \(-\) \(q-2q^{2}+3q^{3}+2q^{4}-q^{5}-6q^{6}+\cdots\)
245.2.a.c \(1\) \(1.956\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(-\) \(-\) \(q-q^{3}-2q^{4}+q^{5}-2q^{9}-3q^{11}+\cdots\)
245.2.a.d \(2\) \(1.956\) \(\Q(\sqrt{17}) \) None \(-1\) \(1\) \(-2\) \(0\) \(+\) \(-\) \(q-\beta q^{2}+(1-\beta )q^{3}+(2+\beta )q^{4}-q^{5}+\cdots\)
245.2.a.e \(2\) \(1.956\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(q+\beta q^{2}+(-1-\beta )q^{3}-q^{5}+(-2-\beta )q^{6}+\cdots\)
245.2.a.f \(2\) \(1.956\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(0\) \(-\) \(+\) \(q+\beta q^{2}+(1+\beta )q^{3}+q^{5}+(2+\beta )q^{6}+\cdots\)
245.2.a.g \(2\) \(1.956\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(0\) \(+\) \(-\) \(q+(1+\beta )q^{2}+(-1+\beta )q^{3}+(1+2\beta )q^{4}+\cdots\)
245.2.a.h \(2\) \(1.956\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(2\) \(0\) \(-\) \(+\) \(q+(1+\beta )q^{2}+(1-\beta )q^{3}+(1+2\beta )q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(245))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(245)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)