Properties

Label 4005.2.a
Level 4005
Weight 2
Character orbit a
Rep. character \(\chi_{4005}(1,\cdot)\)
Character field \(\Q\)
Dimension 148
Newforms 24
Sturm bound 1080
Trace bound 5

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Defining parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)
Character field: \(\Q\)
Newforms: \( 24 \)
Sturm bound: \(1080\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4005))\).

Total New Old
Modular forms 548 148 400
Cusp forms 533 148 385
Eisenstein series 15 0 15

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

\(3\)\(5\)\(89\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(13\)
\(+\)\(+\)\(-\)\(-\)\(17\)
\(+\)\(-\)\(+\)\(-\)\(17\)
\(+\)\(-\)\(-\)\(+\)\(13\)
\(-\)\(+\)\(+\)\(-\)\(23\)
\(-\)\(+\)\(-\)\(+\)\(21\)
\(-\)\(-\)\(+\)\(+\)\(21\)
\(-\)\(-\)\(-\)\(-\)\(23\)
Plus space\(+\)\(68\)
Minus space\(-\)\(80\)

Trace form

\( 148q - 4q^{2} + 152q^{4} + O(q^{10}) \) \( 148q - 4q^{2} + 152q^{4} + 4q^{10} - 8q^{11} + 4q^{13} - 12q^{14} + 160q^{16} - 12q^{17} + 12q^{19} - 16q^{22} + 12q^{23} + 148q^{25} + 8q^{26} - 24q^{28} - 24q^{29} - 44q^{32} + 4q^{35} + 16q^{37} - 4q^{38} - 20q^{43} - 28q^{44} - 32q^{46} + 4q^{47} + 188q^{49} - 4q^{50} - 60q^{52} - 56q^{53} + 8q^{55} + 12q^{56} - 32q^{58} + 4q^{59} - 12q^{61} - 16q^{62} + 152q^{64} + 12q^{65} - 16q^{67} - 60q^{68} + 20q^{70} + 24q^{71} + 12q^{73} + 8q^{74} + 28q^{76} - 20q^{77} - 12q^{79} + 8q^{83} - 52q^{86} - 48q^{88} - 28q^{91} + 44q^{92} + 20q^{94} + 16q^{95} + 56q^{97} + 32q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4005))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 89
4005.2.a.a \(1\) \(31.980\) \(\Q\) None \(-1\) \(0\) \(1\) \(4\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{4}+q^{5}+4q^{7}+3q^{8}-q^{10}+\cdots\)
4005.2.a.b \(1\) \(31.980\) \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) \(+\) \(+\) \(+\) \(q-2q^{4}-q^{5}-4q^{7}-2q^{11}+4q^{13}+\cdots\)
4005.2.a.c \(1\) \(31.980\) \(\Q\) None \(0\) \(0\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(q-2q^{4}+q^{5}-4q^{7}+2q^{11}+4q^{13}+\cdots\)
4005.2.a.d \(1\) \(31.980\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-4q^{11}+\cdots\)
4005.2.a.e \(2\) \(31.980\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}-\beta q^{7}+\cdots\)
4005.2.a.f \(2\) \(31.980\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+q^{4}-q^{5}+(-1+\beta )q^{7}-\beta q^{8}+\cdots\)
4005.2.a.g \(2\) \(31.980\) \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+(2+\beta )q^{4}-q^{5}+(4+\beta )q^{8}+\cdots\)
4005.2.a.h \(2\) \(31.980\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}+q^{5}+(1+\beta )q^{7}-3q^{8}+\cdots\)
4005.2.a.i \(3\) \(31.980\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(-3\) \(3\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(1+\beta _{2})q^{7}+\cdots\)
4005.2.a.j \(3\) \(31.980\) \(\Q(\zeta_{14})^+\) None \(2\) \(0\) \(-3\) \(-5\) \(-\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
4005.2.a.k \(4\) \(31.980\) 4.4.8069.1 None \(-1\) \(0\) \(-4\) \(12\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+3q^{7}+\cdots\)
4005.2.a.l \(4\) \(31.980\) 4.4.725.1 None \(-1\) \(0\) \(4\) \(2\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
4005.2.a.m \(4\) \(31.980\) 4.4.2777.1 None \(0\) \(0\) \(4\) \(-7\) \(-\) \(-\) \(+\) \(q-\beta _{2}q^{2}+(1-\beta _{3})q^{4}+q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
4005.2.a.n \(6\) \(31.980\) 6.6.10407557.1 None \(4\) \(0\) \(6\) \(1\) \(-\) \(-\) \(-\) \(q+(1+\beta _{2})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+q^{5}+\cdots\)
4005.2.a.o \(7\) \(31.980\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4\) \(0\) \(-7\) \(-16\) \(-\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{3})q^{4}-q^{5}+\cdots\)
4005.2.a.p \(8\) \(31.980\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(0\) \(8\) \(-6\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
4005.2.a.q \(9\) \(31.980\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-5\) \(0\) \(9\) \(-3\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4005.2.a.r \(10\) \(31.980\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-6\) \(0\) \(-10\) \(7\) \(-\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4005.2.a.s \(10\) \(31.980\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-1\) \(0\) \(-10\) \(-1\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{6}q^{7}+\cdots\)
4005.2.a.t \(10\) \(31.980\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(10\) \(9\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots\)
4005.2.a.u \(12\) \(31.980\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(0\) \(12\) \(-8\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
4005.2.a.v \(12\) \(31.980\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(0\) \(-12\) \(-8\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
4005.2.a.w \(17\) \(31.980\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-5\) \(0\) \(-17\) \(12\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{8}+\cdots)q^{7}+\cdots\)
4005.2.a.x \(17\) \(31.980\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(5\) \(0\) \(17\) \(12\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1+\beta _{8}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(267))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(445))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(801))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1335))\)\(^{\oplus 2}\)