Properties

Label 4011.2.a
Level 4011
Weight 2
Character orbit a
Rep. character \(\chi_{4011}(1,\cdot)\)
Character field \(\Q\)
Dimension 191
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 13 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\) into newform subspaces

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

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