Properties

Label 1441.2.a
Level $1441$
Weight $2$
Character orbit 1441.a
Rep. character $\chi_{1441}(1,\cdot)$
Character field $\Q$
Dimension $107$
Newform subspaces $6$
Sturm bound $264$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(264\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1441))\).

Total New Old
Modular forms 134 107 27
Cusp forms 131 107 24
Eisenstein series 3 0 3

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

\(11\)\(131\)FrickeDim.
\(+\)\(+\)\(+\)\(24\)
\(+\)\(-\)\(-\)\(31\)
\(-\)\(+\)\(-\)\(29\)
\(-\)\(-\)\(+\)\(23\)
Plus space\(+\)\(47\)
Minus space\(-\)\(60\)

Trace form

\( 107 q + q^{2} - 2 q^{3} + 99 q^{4} - 8 q^{5} - 4 q^{6} - 4 q^{7} + 9 q^{8} + 101 q^{9} + O(q^{10}) \) \( 107 q + q^{2} - 2 q^{3} + 99 q^{4} - 8 q^{5} - 4 q^{6} - 4 q^{7} + 9 q^{8} + 101 q^{9} - 2 q^{10} - 3 q^{11} + 8 q^{12} - 22 q^{13} + 8 q^{14} - 6 q^{15} + 87 q^{16} - 10 q^{17} + 29 q^{18} - 16 q^{19} - 6 q^{20} - 36 q^{21} + 3 q^{22} + 14 q^{23} + 12 q^{24} + 87 q^{25} + 22 q^{26} - 2 q^{27} + 16 q^{28} - 18 q^{29} + 64 q^{30} - 22 q^{31} + 49 q^{32} - 2 q^{33} - 30 q^{34} + 12 q^{35} + 79 q^{36} - 36 q^{37} + 12 q^{38} + 8 q^{39} - 34 q^{40} + 10 q^{41} + 4 q^{42} - 12 q^{43} - 11 q^{44} - 58 q^{45} - 32 q^{46} - 4 q^{47} + 4 q^{48} + 71 q^{49} - 5 q^{50} + 36 q^{51} - 42 q^{52} - 10 q^{53} - 44 q^{54} - 8 q^{55} + 52 q^{56} - 16 q^{57} + 26 q^{58} - 6 q^{59} - 48 q^{60} - 74 q^{61} + 64 q^{62} - 12 q^{63} + 71 q^{64} - 8 q^{65} - 8 q^{66} + 14 q^{67} - 10 q^{68} - 38 q^{69} + 32 q^{70} + 34 q^{71} + 109 q^{72} - 22 q^{73} - 34 q^{74} + 8 q^{75} - 36 q^{76} - 100 q^{78} - 4 q^{79} - 30 q^{80} + 67 q^{81} + 42 q^{82} + 44 q^{83} - 108 q^{84} - 36 q^{85} + 68 q^{86} + 16 q^{87} - 9 q^{88} - 64 q^{89} - 18 q^{90} - 32 q^{91} + 16 q^{92} + 2 q^{93} - 12 q^{94} + 20 q^{95} - 8 q^{96} - 44 q^{97} - 91 q^{98} - 9 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1441))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11 131
1441.2.a.a $1$ $11.506$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $+$ $+$ \(q-q^{3}-2q^{4}+q^{5}+2q^{7}-2q^{9}-q^{11}+\cdots\)
1441.2.a.b $1$ $11.506$ \(\Q\) None \(2\) \(3\) \(-2\) \(3\) $-$ $+$ \(q+2q^{2}+3q^{3}+2q^{4}-2q^{5}+6q^{6}+\cdots\)
1441.2.a.c $23$ $11.506$ None \(-7\) \(-3\) \(-9\) \(-12\) $-$ $-$
1441.2.a.d $23$ $11.506$ None \(-7\) \(-3\) \(-9\) \(-8\) $+$ $+$
1441.2.a.e $28$ $11.506$ None \(7\) \(-2\) \(3\) \(7\) $-$ $+$
1441.2.a.f $31$ $11.506$ None \(6\) \(4\) \(8\) \(4\) $+$ $-$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1441))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1441)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(131))\)\(^{\oplus 2}\)