Properties

Label 8043.2.a
Level 8043
Weight 2
Character orbit a
Rep. character \(\chi_{8043}(1,\cdot)\)
Character field \(\Q\)
Dimension 383
Newforms 21
Sturm bound 2048
Trace bound 11

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Defining parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)
Character field: \(\Q\)
Newforms: \( 21 \)
Sturm bound: \(2048\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8043))\).

Total New Old
Modular forms 1028 383 645
Cusp forms 1021 383 638
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.

\(3\)\(7\)\(383\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(46\)
\(+\)\(+\)\(-\)\(-\)\(50\)
\(+\)\(-\)\(+\)\(-\)\(54\)
\(+\)\(-\)\(-\)\(+\)\(42\)
\(-\)\(+\)\(+\)\(-\)\(49\)
\(-\)\(+\)\(-\)\(+\)\(45\)
\(-\)\(-\)\(+\)\(+\)\(43\)
\(-\)\(-\)\(-\)\(-\)\(54\)
Plus space\(+\)\(176\)
Minus space\(-\)\(207\)

Trace form

\(383q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 385q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 383q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(383q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 385q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 383q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 18q^{13} \) \(\mathstrut +\mathstrut q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 377q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 3q^{21} \) \(\mathstrut -\mathstrut 20q^{22} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 409q^{25} \) \(\mathstrut -\mathstrut 18q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut +\mathstrut 5q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 385q^{36} \) \(\mathstrut +\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 60q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 66q^{40} \) \(\mathstrut +\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 10q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 24q^{47} \) \(\mathstrut -\mathstrut 31q^{48} \) \(\mathstrut +\mathstrut 383q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 14q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 42q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut 48q^{62} \) \(\mathstrut +\mathstrut 3q^{63} \) \(\mathstrut +\mathstrut 337q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut +\mathstrut 36q^{67} \) \(\mathstrut +\mathstrut 10q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut +\mathstrut 16q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut +\mathstrut 22q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut +\mathstrut 28q^{76} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut -\mathstrut 34q^{80} \) \(\mathstrut +\mathstrut 383q^{81} \) \(\mathstrut -\mathstrut 30q^{82} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 5q^{84} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 36q^{86} \) \(\mathstrut +\mathstrut 2q^{87} \) \(\mathstrut -\mathstrut 92q^{88} \) \(\mathstrut +\mathstrut 38q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 80q^{92} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 64q^{95} \) \(\mathstrut -\mathstrut 23q^{96} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut +\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8043))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 383
8043.2.a.a \(1\) \(64.224\) \(\Q\) None \(-2\) \(1\) \(-3\) \(-1\) \(-\) \(+\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots\)
8043.2.a.b \(1\) \(64.224\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
8043.2.a.c \(1\) \(64.224\) \(\Q\) None \(-1\) \(1\) \(2\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
8043.2.a.d \(1\) \(64.224\) \(\Q\) None \(-1\) \(1\) \(4\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}-q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
8043.2.a.e \(1\) \(64.224\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-5q^{11}+\cdots\)
8043.2.a.f \(1\) \(64.224\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}-3q^{11}+\cdots\)
8043.2.a.g \(1\) \(64.224\) \(\Q\) None \(0\) \(1\) \(2\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{3}-2q^{4}+2q^{5}-q^{7}+q^{9}+3q^{11}+\cdots\)
8043.2.a.h \(1\) \(64.224\) \(\Q\) None \(0\) \(1\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{4}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots\)
8043.2.a.i \(1\) \(64.224\) \(\Q\) None \(2\) \(-1\) \(3\) \(1\) \(+\) \(-\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots\)
8043.2.a.j \(1\) \(64.224\) \(\Q\) None \(2\) \(-1\) \(3\) \(1\) \(+\) \(-\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots\)
8043.2.a.k \(1\) \(64.224\) \(\Q\) None \(2\) \(1\) \(1\) \(-1\) \(-\) \(+\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
8043.2.a.l \(2\) \(64.224\) \(\Q(\sqrt{17}) \) None \(-1\) \(2\) \(1\) \(2\) \(-\) \(-\) \(+\) \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
8043.2.a.m \(3\) \(64.224\) 3.3.148.1 None \(-1\) \(3\) \(-2\) \(-3\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
8043.2.a.n \(40\) \(64.224\) None \(-9\) \(40\) \(-27\) \(40\) \(-\) \(-\) \(+\)
8043.2.a.o \(41\) \(64.224\) None \(-4\) \(-41\) \(5\) \(41\) \(+\) \(-\) \(-\)
8043.2.a.p \(41\) \(64.224\) None \(7\) \(41\) \(17\) \(-41\) \(-\) \(+\) \(+\)
8043.2.a.q \(44\) \(64.224\) None \(-4\) \(44\) \(-16\) \(-44\) \(-\) \(+\) \(-\)
8043.2.a.r \(46\) \(64.224\) None \(3\) \(-46\) \(-9\) \(-46\) \(+\) \(+\) \(+\)
8043.2.a.s \(50\) \(64.224\) None \(-1\) \(-50\) \(11\) \(-50\) \(+\) \(+\) \(-\)
8043.2.a.t \(52\) \(64.224\) None \(3\) \(-52\) \(-7\) \(52\) \(+\) \(-\) \(+\)
8043.2.a.u \(53\) \(64.224\) None \(11\) \(53\) \(24\) \(53\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8043))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8043)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(383))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1149))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2681))\)\(^{\oplus 2}\)