Properties

Label 285.2.a
Level $285$
Weight $2$
Character orbit 285.a
Rep. character $\chi_{285}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $7$
Sturm bound $80$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(80\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(285))\).

Total New Old
Modular forms 44 11 33
Cusp forms 37 11 26
Eisenstein series 7 0 7

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

\(3\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(9\)

Trace form

\( 11q + 5q^{2} - q^{3} + 13q^{4} - q^{5} - 3q^{6} + 9q^{8} + 11q^{9} + O(q^{10}) \) \( 11q + 5q^{2} - q^{3} + 13q^{4} - q^{5} - 3q^{6} + 9q^{8} + 11q^{9} - 3q^{10} + 12q^{11} - 7q^{12} - 6q^{13} - q^{15} + 21q^{16} - 10q^{17} + 5q^{18} - q^{19} + 9q^{20} - 8q^{21} + 4q^{22} + 9q^{24} + 11q^{25} - 26q^{26} - q^{27} - 8q^{28} + 10q^{29} + q^{30} - 7q^{32} - 4q^{33} - 6q^{34} + 13q^{36} + 2q^{37} - 3q^{38} - 6q^{39} - 15q^{40} - 18q^{41} + 8q^{42} + 20q^{43} + 12q^{44} - q^{45} - 32q^{46} + 8q^{47} - 31q^{48} - 13q^{49} + 5q^{50} + 14q^{51} - 42q^{52} + 10q^{53} - 3q^{54} + 20q^{55} - 48q^{56} + 3q^{57} - 42q^{58} + 52q^{59} - 7q^{60} - 22q^{61} - 56q^{62} + 21q^{64} - 6q^{65} - 20q^{66} + 12q^{67} - 70q^{68} - 8q^{69} - 8q^{70} + 24q^{71} + 9q^{72} - 10q^{73} - 26q^{74} - q^{75} - 7q^{76} + 8q^{77} - 2q^{78} + q^{80} + 11q^{81} + 2q^{82} + 4q^{83} - 8q^{84} - 2q^{85} + 4q^{86} + 10q^{87} + 20q^{88} - 18q^{89} - 3q^{90} + 48q^{91} + 64q^{92} - 16q^{93} + 56q^{94} - q^{95} - 15q^{96} - 58q^{97} + 29q^{98} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(285))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 19
285.2.a.a \(1\) \(2.276\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
285.2.a.b \(1\) \(2.276\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
285.2.a.c \(1\) \(2.276\) \(\Q\) None \(1\) \(-1\) \(1\) \(4\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
285.2.a.d \(2\) \(2.276\) \(\Q(\sqrt{7}) \) None \(0\) \(-2\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(q+\beta q^{2}-q^{3}+5q^{4}+q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
285.2.a.e \(2\) \(2.276\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-2\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+q^{3}+q^{4}+q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
285.2.a.f \(2\) \(2.276\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(4\) \(+\) \(+\) \(-\) \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
285.2.a.g \(2\) \(2.276\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(285))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(285)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 2}\)