Properties

Label 663.2.a
Level $663$
Weight $2$
Character orbit 663.a
Rep. character $\chi_{663}(1,\cdot)$
Character field $\Q$
Dimension $31$
Newform subspaces $9$
Sturm bound $168$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 663 = 3 \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 663.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(168\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(663))\).

Total New Old
Modular forms 88 31 57
Cusp forms 81 31 50
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.

\(3\)\(13\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(8\)
Minus space\(-\)\(23\)

Trace form

\( 31 q + 5 q^{2} - q^{3} + 33 q^{4} - 6 q^{5} + q^{6} + 8 q^{7} + 33 q^{8} + 31 q^{9} + O(q^{10}) \) \( 31 q + 5 q^{2} - q^{3} + 33 q^{4} - 6 q^{5} + q^{6} + 8 q^{7} + 33 q^{8} + 31 q^{9} + 22 q^{10} + 4 q^{11} + q^{12} - q^{13} + 8 q^{14} + 2 q^{15} + 33 q^{16} - q^{17} + 5 q^{18} - 20 q^{19} - 18 q^{20} - 8 q^{21} - 4 q^{22} - 3 q^{24} + 33 q^{25} - 3 q^{26} - q^{27} + 16 q^{28} + 10 q^{29} - 10 q^{30} + 41 q^{32} + 12 q^{33} + 5 q^{34} + 24 q^{35} + 33 q^{36} + 2 q^{37} - 4 q^{38} + 7 q^{39} + 6 q^{40} - 18 q^{41} - 16 q^{42} + 20 q^{43} + 12 q^{44} - 6 q^{45} + 24 q^{46} + 48 q^{47} - 15 q^{48} + 7 q^{49} + 35 q^{50} - q^{51} + q^{52} + 18 q^{53} + q^{54} - 8 q^{55} - 12 q^{57} - 42 q^{58} - 20 q^{59} - 18 q^{60} - 38 q^{61} - 32 q^{62} + 8 q^{63} + 73 q^{64} + 2 q^{65} + 12 q^{66} + 28 q^{67} - 7 q^{68} - 16 q^{69} - 64 q^{70} - 16 q^{71} + 33 q^{72} + 6 q^{73} - 2 q^{74} - 15 q^{75} - 92 q^{76} - 24 q^{77} + q^{78} - 32 q^{79} - 114 q^{80} + 31 q^{81} - 6 q^{82} - 44 q^{83} - 32 q^{84} + 2 q^{85} + 20 q^{86} - 6 q^{87} - 28 q^{88} - 34 q^{89} + 22 q^{90} + 8 q^{91} - 32 q^{92} - 16 q^{93} - 72 q^{94} + 24 q^{95} - 35 q^{96} + 14 q^{97} - 3 q^{98} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(663))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 13 17
663.2.a.a $1$ $5.294$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $-$ $-$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots\)
663.2.a.b $1$ $5.294$ \(\Q\) None \(-1\) \(1\) \(0\) \(-2\) $-$ $+$ $-$ \(q-q^{2}+q^{3}-q^{4}-q^{6}-2q^{7}+3q^{8}+\cdots\)
663.2.a.c $1$ $5.294$ \(\Q\) None \(1\) \(-1\) \(-4\) \(2\) $+$ $+$ $-$ \(q+q^{2}-q^{3}-q^{4}-4q^{5}-q^{6}+2q^{7}+\cdots\)
663.2.a.d $3$ $5.294$ 3.3.148.1 None \(-3\) \(3\) \(-6\) \(-2\) $-$ $-$ $+$ \(q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
663.2.a.e $3$ $5.294$ 3.3.148.1 None \(-1\) \(-3\) \(0\) \(-4\) $+$ $+$ $+$ \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
663.2.a.f $5$ $5.294$ 5.5.1004368.1 None \(1\) \(-5\) \(2\) \(8\) $+$ $-$ $+$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
663.2.a.g $5$ $5.294$ 5.5.153424.1 None \(3\) \(5\) \(0\) \(2\) $-$ $+$ $+$ \(q+(1+\beta _{3})q^{2}+q^{3}+(2+\beta _{3}-\beta _{4})q^{4}+\cdots\)
663.2.a.h $6$ $5.294$ 6.6.83831632.1 None \(2\) \(-6\) \(0\) \(2\) $+$ $+$ $-$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
663.2.a.i $6$ $5.294$ 6.6.15187408.1 None \(4\) \(6\) \(4\) \(2\) $-$ $-$ $-$ \(q+(1-\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(663))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(663)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(221))\)\(^{\oplus 2}\)