Properties

Label 4011.2.a
Level 4011
Weight 2
Character orbit a
Rep. character \(\chi_{4011}(1,\cdot)\)
Character field \(\Q\)
Dimension 191
Newforms 13
Sturm bound 1024
Trace bound 2

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Defining parameters

Level: \( N \) = \( 4011 = 3 \cdot 7 \cdot 191 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4011.a (trivial)
Character field: \(\Q\)
Newforms: \( 13 \)
Sturm bound: \(1024\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4011))\).

Total New Old
Modular forms 516 191 325
Cusp forms 509 191 318
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.

\(3\)\(7\)\(191\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(19\)
\(+\)\(+\)\(-\)\(-\)\(29\)
\(+\)\(-\)\(+\)\(-\)\(29\)
\(+\)\(-\)\(-\)\(+\)\(19\)
\(-\)\(+\)\(+\)\(-\)\(29\)
\(-\)\(+\)\(-\)\(+\)\(19\)
\(-\)\(-\)\(+\)\(+\)\(19\)
\(-\)\(-\)\(-\)\(-\)\(28\)
Plus space\(+\)\(76\)
Minus space\(-\)\(115\)

Trace form

\(191q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 197q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 191q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(191q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 197q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 191q^{9} \) \(\mathstrut +\mathstrut 14q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 213q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 38q^{20} \) \(\mathstrut -\mathstrut q^{21} \) \(\mathstrut +\mathstrut 20q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 209q^{25} \) \(\mathstrut +\mathstrut 22q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut +\mathstrut 10q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 5q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 197q^{36} \) \(\mathstrut -\mathstrut 14q^{37} \) \(\mathstrut -\mathstrut 60q^{38} \) \(\mathstrut +\mathstrut 18q^{39} \) \(\mathstrut +\mathstrut 46q^{40} \) \(\mathstrut +\mathstrut 22q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 52q^{44} \) \(\mathstrut +\mathstrut 10q^{45} \) \(\mathstrut -\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut +\mathstrut q^{48} \) \(\mathstrut +\mathstrut 191q^{49} \) \(\mathstrut +\mathstrut 7q^{50} \) \(\mathstrut +\mathstrut 14q^{51} \) \(\mathstrut +\mathstrut 22q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 72q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 38q^{60} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 205q^{64} \) \(\mathstrut +\mathstrut 52q^{65} \) \(\mathstrut -\mathstrut 4q^{66} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 10q^{68} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut +\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 3q^{72} \) \(\mathstrut +\mathstrut 38q^{73} \) \(\mathstrut -\mathstrut 26q^{74} \) \(\mathstrut +\mathstrut 17q^{75} \) \(\mathstrut +\mathstrut 76q^{76} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 10q^{78} \) \(\mathstrut +\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 126q^{80} \) \(\mathstrut +\mathstrut 191q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut +\mathstrut 68q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut +\mathstrut 12q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 18q^{87} \) \(\mathstrut -\mathstrut 28q^{88} \) \(\mathstrut +\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 16q^{92} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 56q^{94} \) \(\mathstrut +\mathstrut 32q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 50q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 191
4011.2.a.a \(1\) \(32.028\) \(\Q\) None \(-2\) \(1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
4011.2.a.b \(1\) \(32.028\) \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4011.2.a.c \(1\) \(32.028\) \(\Q\) None \(0\) \(1\) \(-4\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{4}-4q^{5}-q^{7}+q^{9}-3q^{11}+\cdots\)
4011.2.a.d \(1\) \(32.028\) \(\Q\) None \(2\) \(-1\) \(4\) \(1\) \(+\) \(-\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}+4q^{5}-2q^{6}+\cdots\)
4011.2.a.e \(3\) \(32.028\) 3.3.229.1 None \(0\) \(-3\) \(2\) \(-3\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
4011.2.a.f \(18\) \(32.028\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-6\) \(18\) \(-21\) \(18\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4011.2.a.g \(18\) \(32.028\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-3\) \(18\) \(-10\) \(-18\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{10}+\cdots)q^{5}+\cdots\)
4011.2.a.h \(19\) \(32.028\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(-1\) \(-19\) \(-4\) \(-19\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
4011.2.a.i \(19\) \(32.028\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(3\) \(-19\) \(-12\) \(19\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{8}+\cdots)q^{5}+\cdots\)
4011.2.a.j \(26\) \(32.028\) None \(0\) \(-26\) \(2\) \(-26\) \(+\) \(+\) \(-\)
4011.2.a.k \(27\) \(32.028\) None \(9\) \(27\) \(23\) \(27\) \(-\) \(-\) \(-\)
4011.2.a.l \(28\) \(32.028\) None \(-6\) \(-28\) \(8\) \(28\) \(+\) \(-\) \(+\)
4011.2.a.m \(29\) \(32.028\) None \(6\) \(29\) \(22\) \(-29\) \(-\) \(+\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4011))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4011)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(191))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(573))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1337))\)\(^{\oplus 2}\)