Properties

Label 6025.2.a
Level 6025
Weight 2
Character orbit a
Rep. character \(\chi_{6025}(1,\cdot)\)
Character field \(\Q\)
Dimension 380
Newforms 17
Sturm bound 1210
Trace bound 3

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Defining parameters

Level: \( N \) = \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6025.a (trivial)
Character field: \(\Q\)
Newforms: \( 17 \)
Sturm bound: \(1210\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6025))\).

Total New Old
Modular forms 610 380 230
Cusp forms 599 380 219
Eisenstein series 11 0 11

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

\(5\)\(241\)FrickeDim.
\(+\)\(+\)\(+\)\(87\)
\(+\)\(-\)\(-\)\(93\)
\(-\)\(+\)\(-\)\(106\)
\(-\)\(-\)\(+\)\(94\)
Plus space\(+\)\(181\)
Minus space\(-\)\(199\)

Trace form

\(380q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 382q^{4} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 374q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(380q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 382q^{4} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 374q^{9} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 378q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 2q^{22} \) \(\mathstrut -\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 14q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 4q^{29} \) \(\mathstrut -\mathstrut 10q^{31} \) \(\mathstrut +\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 10q^{34} \) \(\mathstrut +\mathstrut 356q^{36} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 30q^{39} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 42q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 18q^{44} \) \(\mathstrut +\mathstrut 46q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 26q^{48} \) \(\mathstrut +\mathstrut 370q^{49} \) \(\mathstrut -\mathstrut 50q^{51} \) \(\mathstrut +\mathstrut 14q^{53} \) \(\mathstrut +\mathstrut 8q^{54} \) \(\mathstrut -\mathstrut 42q^{56} \) \(\mathstrut -\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 42q^{58} \) \(\mathstrut -\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut +\mathstrut 16q^{62} \) \(\mathstrut +\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 390q^{64} \) \(\mathstrut -\mathstrut 42q^{66} \) \(\mathstrut -\mathstrut 24q^{67} \) \(\mathstrut +\mathstrut 60q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 78q^{72} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 60q^{76} \) \(\mathstrut +\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 26q^{78} \) \(\mathstrut +\mathstrut 18q^{79} \) \(\mathstrut +\mathstrut 356q^{81} \) \(\mathstrut +\mathstrut 22q^{82} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 36q^{84} \) \(\mathstrut +\mathstrut 22q^{86} \) \(\mathstrut -\mathstrut 12q^{87} \) \(\mathstrut +\mathstrut 50q^{88} \) \(\mathstrut +\mathstrut 18q^{89} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 18q^{93} \) \(\mathstrut +\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 56q^{98} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 241
6025.2.a.a \(2\) \(48.110\) \(\Q(\sqrt{5}) \) None \(-2\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}-q^{4}-\beta q^{6}+(-2+2\beta )q^{7}+\cdots\)
6025.2.a.b \(2\) \(48.110\) \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(0\) \(2\) \(-\) \(-\) \(q+(1-2\beta )q^{2}+(-2+\beta )q^{3}+3q^{4}+\cdots\)
6025.2.a.c \(2\) \(48.110\) \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(0\) \(-2\) \(-\) \(-\) \(q+(1-2\beta )q^{2}+(1+\beta )q^{3}+3q^{4}+(-1+\cdots)q^{6}+\cdots\)
6025.2.a.d \(2\) \(48.110\) \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(0\) \(2\) \(-\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}-q^{4}+(-1+\beta )q^{6}+\cdots\)
6025.2.a.e \(5\) \(48.110\) 5.5.38569.1 None \(1\) \(5\) \(0\) \(10\) \(+\) \(-\) \(q+(\beta _{1}+\beta _{3})q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4})q^{3}+\cdots\)
6025.2.a.f \(7\) \(48.110\) 7.7.31056073.1 None \(4\) \(3\) \(0\) \(7\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}-\beta _{6}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
6025.2.a.g \(11\) \(48.110\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(4\) \(8\) \(0\) \(9\) \(+\) \(-\) \(q+(1-\beta _{1}+\beta _{2})q^{2}+(1+\beta _{2}+\beta _{3})q^{3}+\cdots\)
6025.2.a.h \(12\) \(48.110\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(-1\) \(0\) \(-3\) \(+\) \(-\) \(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{6}+\cdots\)
6025.2.a.i \(15\) \(48.110\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-2\) \(7\) \(0\) \(3\) \(+\) \(+\) \(q-\beta _{1}q^{2}-\beta _{11}q^{3}+\beta _{2}q^{4}+(-\beta _{8}+\cdots)q^{6}+\cdots\)
6025.2.a.j \(25\) \(48.110\) None \(-6\) \(-15\) \(0\) \(-19\) \(+\) \(+\)
6025.2.a.k \(25\) \(48.110\) None \(4\) \(-9\) \(0\) \(-7\) \(+\) \(-\)
6025.2.a.l \(40\) \(48.110\) None \(-11\) \(-8\) \(0\) \(-16\) \(+\) \(+\)
6025.2.a.m \(40\) \(48.110\) None \(-9\) \(-8\) \(0\) \(-20\) \(-\) \(-\)
6025.2.a.n \(40\) \(48.110\) None \(9\) \(8\) \(0\) \(20\) \(+\) \(-\)
6025.2.a.o \(40\) \(48.110\) None \(11\) \(8\) \(0\) \(16\) \(-\) \(+\)
6025.2.a.p \(46\) \(48.110\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\)
6025.2.a.q \(66\) \(48.110\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(241))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1205))\)\(^{\oplus 2}\)