Properties

Label 4025.2.a
Level 4025
Weight 2
Character orbit a
Rep. character \(\chi_{4025}(1,\cdot)\)
Character field \(\Q\)
Dimension 210
Newforms 31
Sturm bound 960
Trace bound 11

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4025.a (trivial)
Character field: \(\Q\)
Newforms: \( 31 \)
Sturm bound: \(960\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4025))\).

Total New Old
Modular forms 492 210 282
Cusp forms 469 210 259
Eisenstein series 23 0 23

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

\(5\)\(7\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(27\)
\(+\)\(+\)\(-\)\(-\)\(22\)
\(+\)\(-\)\(+\)\(-\)\(31\)
\(+\)\(-\)\(-\)\(+\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(29\)
\(-\)\(+\)\(-\)\(+\)\(27\)
\(-\)\(-\)\(+\)\(+\)\(21\)
\(-\)\(-\)\(-\)\(-\)\(35\)
Plus space\(+\)\(93\)
Minus space\(-\)\(117\)

Trace form

\( 210q - 4q^{3} + 212q^{4} - 10q^{6} - 6q^{8} + 206q^{9} + O(q^{10}) \) \( 210q - 4q^{3} + 212q^{4} - 10q^{6} - 6q^{8} + 206q^{9} - 2q^{12} + 16q^{13} + 232q^{16} + 4q^{17} + 22q^{18} - 12q^{19} + 4q^{21} + 4q^{22} - 6q^{23} + 36q^{24} - 2q^{26} - 28q^{27} - 8q^{29} - 8q^{31} - 12q^{32} - 24q^{33} - 52q^{34} + 258q^{36} + 24q^{37} + 56q^{38} + 24q^{39} - 48q^{41} + 20q^{42} + 8q^{43} + 44q^{44} + 4q^{46} + 24q^{47} + 14q^{48} + 210q^{49} - 24q^{51} + 22q^{52} + 16q^{53} - 26q^{54} - 4q^{57} + 42q^{58} - 60q^{59} + 4q^{61} + 34q^{62} + 262q^{64} + 52q^{66} + 4q^{67} + 36q^{68} + 64q^{71} + 106q^{72} + 8q^{73} - 20q^{74} - 76q^{76} - 22q^{78} + 4q^{79} + 146q^{81} - 26q^{82} - 8q^{83} + 16q^{84} - 24q^{86} + 4q^{87} + 24q^{88} - 4q^{89} + 12q^{91} - 12q^{92} - 44q^{93} + 50q^{94} + 54q^{96} + 8q^{97} + 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4025))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 7 23
4025.2.a.a \(1\) \(32.140\) \(\Q\) None \(-2\) \(-3\) \(0\) \(1\) \(+\) \(-\) \(+\) \(q-2q^{2}-3q^{3}+2q^{4}+6q^{6}+q^{7}+\cdots\)
4025.2.a.b \(1\) \(32.140\) \(\Q\) None \(-2\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}-2q^{9}+\cdots\)
4025.2.a.c \(1\) \(32.140\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q-q^{3}-2q^{4}+q^{7}-2q^{9}-q^{11}+2q^{12}+\cdots\)
4025.2.a.d \(1\) \(32.140\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{4}-q^{7}-2q^{9}-q^{11}-2q^{12}+\cdots\)
4025.2.a.e \(1\) \(32.140\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{4}-q^{7}-3q^{8}-3q^{9}+4q^{11}+\cdots\)
4025.2.a.f \(1\) \(32.140\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{4}+q^{7}-3q^{8}-3q^{9}-4q^{11}+\cdots\)
4025.2.a.g \(1\) \(32.140\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{4}+q^{7}-3q^{8}-3q^{9}+2q^{11}+\cdots\)
4025.2.a.h \(2\) \(32.140\) \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
4025.2.a.i \(2\) \(32.140\) \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
4025.2.a.j \(3\) \(32.140\) 3.3.148.1 None \(1\) \(-2\) \(0\) \(3\) \(+\) \(-\) \(+\) \(q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
4025.2.a.k \(3\) \(32.140\) \(\Q(\zeta_{14})^+\) None \(2\) \(0\) \(0\) \(3\) \(+\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+(-1+\beta _{1}-2\beta _{2})q^{3}+\cdots\)
4025.2.a.l \(4\) \(32.140\) 4.4.2777.1 None \(-3\) \(-6\) \(0\) \(4\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots\)
4025.2.a.m \(4\) \(32.140\) 4.4.7537.1 None \(-1\) \(-4\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4025.2.a.n \(4\) \(32.140\) 4.4.22545.1 None \(1\) \(0\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(3+\beta _{3})q^{4}+\cdots\)
4025.2.a.o \(4\) \(32.140\) 4.4.2777.1 None \(2\) \(5\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q+(1-\beta _{3})q^{2}+(1+\beta _{1})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
4025.2.a.p \(5\) \(32.140\) 5.5.2147108.1 None \(-2\) \(0\) \(0\) \(-5\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
4025.2.a.q \(5\) \(32.140\) 5.5.255877.1 None \(1\) \(4\) \(0\) \(-5\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4025.2.a.r \(5\) \(32.140\) 5.5.122821.1 None \(3\) \(6\) \(0\) \(5\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(\beta _{3}+\beta _{4})q^{4}+\cdots\)
4025.2.a.s \(8\) \(32.140\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-3\) \(-2\) \(0\) \(8\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{6}+\cdots)q^{6}+\cdots\)
4025.2.a.t \(8\) \(32.140\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(-7\) \(0\) \(-8\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4025.2.a.u \(8\) \(32.140\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(-4\) \(0\) \(8\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4025.2.a.v \(8\) \(32.140\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(4\) \(0\) \(-8\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4025.2.a.w \(8\) \(32.140\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(2\) \(0\) \(-8\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{6}+\cdots)q^{6}+\cdots\)
4025.2.a.x \(12\) \(32.140\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(0\) \(0\) \(12\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
4025.2.a.y \(12\) \(32.140\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(0\) \(0\) \(-12\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
4025.2.a.z \(14\) \(32.140\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-3\) \(-4\) \(0\) \(-14\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
4025.2.a.ba \(14\) \(32.140\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-1\) \(-6\) \(0\) \(-14\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
4025.2.a.bb \(14\) \(32.140\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(1\) \(6\) \(0\) \(14\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
4025.2.a.bc \(14\) \(32.140\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(3\) \(4\) \(0\) \(14\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
4025.2.a.bd \(21\) \(32.140\) None \(-2\) \(1\) \(0\) \(-21\) \(-\) \(+\) \(+\)
4025.2.a.be \(21\) \(32.140\) None \(2\) \(-1\) \(0\) \(21\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(805))\)\(^{\oplus 2}\)