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

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

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

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