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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 19
285.2.a.a 285.a 1.a $1$ $2.276$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
285.2.a.b 285.a 1.a $1$ $2.276$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
285.2.a.c 285.a 1.a $1$ $2.276$ \(\Q\) None \(1\) \(-1\) \(1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
285.2.a.d 285.a 1.a $2$ $2.276$ \(\Q(\sqrt{7}) \) None \(0\) \(-2\) \(2\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+5q^{4}+q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
285.2.a.e 285.a 1.a $2$ $2.276$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{4}+q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
285.2.a.f 285.a 1.a $2$ $2.276$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
285.2.a.g 285.a 1.a $2$ $2.276$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)

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

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