Properties

Label 4725.2.a
Level 4725
Weight 2
Character orbit a
Rep. character \(\chi_{4725}(1,\cdot)\)
Character field \(\Q\)
Dimension 152
Newforms 58
Sturm bound 1440
Trace bound 13

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Defining parameters

Level: \( N \) = \( 4725 = 3^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4725.a (trivial)
Character field: \(\Q\)
Newforms: \( 58 \)
Sturm bound: \(1440\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(11\), \(13\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4725))\).

Total New Old
Modular forms 756 152 604
Cusp forms 685 152 533
Eisenstein series 71 0 71

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

\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(17\)
\(+\)\(+\)\(-\)\(-\)\(19\)
\(+\)\(-\)\(+\)\(-\)\(22\)
\(+\)\(-\)\(-\)\(+\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(+\)\(17\)
\(-\)\(-\)\(+\)\(+\)\(18\)
\(-\)\(-\)\(-\)\(-\)\(22\)
Plus space\(+\)\(70\)
Minus space\(-\)\(82\)

Trace form

\(152q \) \(\mathstrut +\mathstrut 148q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(152q \) \(\mathstrut +\mathstrut 148q^{4} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 116q^{16} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 28q^{22} \) \(\mathstrut -\mathstrut 16q^{28} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 36q^{34} \) \(\mathstrut +\mathstrut 48q^{37} \) \(\mathstrut -\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut +\mathstrut 152q^{49} \) \(\mathstrut +\mathstrut 40q^{52} \) \(\mathstrut +\mathstrut 16q^{58} \) \(\mathstrut +\mathstrut 36q^{61} \) \(\mathstrut +\mathstrut 100q^{64} \) \(\mathstrut -\mathstrut 48q^{67} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut -\mathstrut 44q^{79} \) \(\mathstrut +\mathstrut 44q^{82} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut +\mathstrut 124q^{94} \) \(\mathstrut -\mathstrut 12q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4725))\) 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 7
4725.2.a.a \(1\) \(37.729\) \(\Q\) None \(-2\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-2q^{2}+2q^{4}-q^{7}-3q^{13}+2q^{14}+\cdots\)
4725.2.a.b \(1\) \(37.729\) \(\Q\) None \(-2\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{2}+2q^{4}+q^{7}+3q^{13}-2q^{14}+\cdots\)
4725.2.a.c \(1\) \(37.729\) \(\Q\) None \(-2\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(q-2q^{2}+2q^{4}+q^{7}+4q^{11}+2q^{13}+\cdots\)
4725.2.a.d \(1\) \(37.729\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{4}-q^{7}+3q^{8}+3q^{11}-3q^{13}+\cdots\)
4725.2.a.e \(1\) \(37.729\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{4}-q^{7}+3q^{8}+3q^{11}+7q^{13}+\cdots\)
4725.2.a.f \(1\) \(37.729\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{4}+q^{7}+3q^{8}-3q^{11}-7q^{13}+\cdots\)
4725.2.a.g \(1\) \(37.729\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{4}+q^{7}+3q^{8}-3q^{11}+3q^{13}+\cdots\)
4725.2.a.h \(1\) \(37.729\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-2q^{4}-q^{7}-6q^{11}+q^{13}+4q^{16}+\cdots\)
4725.2.a.i \(1\) \(37.729\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-2q^{4}-q^{7}-6q^{11}+4q^{13}+4q^{16}+\cdots\)
4725.2.a.j \(1\) \(37.729\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-2q^{4}-q^{7}+6q^{11}+q^{13}+4q^{16}+\cdots\)
4725.2.a.k \(1\) \(37.729\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-2q^{4}-q^{7}+6q^{11}+4q^{13}+4q^{16}+\cdots\)
4725.2.a.l \(1\) \(37.729\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{4}+q^{7}-6q^{11}-q^{13}+4q^{16}+\cdots\)
4725.2.a.m \(1\) \(37.729\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{4}+q^{7}+6q^{11}-q^{13}+4q^{16}+\cdots\)
4725.2.a.n \(1\) \(37.729\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{4}-q^{7}-3q^{8}-3q^{11}-3q^{13}+\cdots\)
4725.2.a.o \(1\) \(37.729\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{4}-q^{7}-3q^{8}-3q^{11}+7q^{13}+\cdots\)
4725.2.a.p \(1\) \(37.729\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}+q^{7}-3q^{8}+3q^{11}-7q^{13}+\cdots\)
4725.2.a.q \(1\) \(37.729\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}+q^{7}-3q^{8}+3q^{11}+3q^{13}+\cdots\)
4725.2.a.r \(1\) \(37.729\) \(\Q\) None \(2\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q+2q^{2}+2q^{4}-q^{7}-3q^{13}-2q^{14}+\cdots\)
4725.2.a.s \(1\) \(37.729\) \(\Q\) None \(2\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+2q^{2}+2q^{4}+q^{7}-4q^{11}+2q^{13}+\cdots\)
4725.2.a.t \(1\) \(37.729\) \(\Q\) None \(2\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+2q^{2}+2q^{4}+q^{7}+3q^{13}+2q^{14}+\cdots\)
4725.2.a.u \(2\) \(37.729\) \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q+(-1-\beta )q^{2}+3\beta q^{4}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
4725.2.a.v \(2\) \(37.729\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{7}+(-3+\cdots)q^{8}+\cdots\)
4725.2.a.w \(2\) \(37.729\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots\)
4725.2.a.x \(2\) \(37.729\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots\)
4725.2.a.y \(2\) \(37.729\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots\)
4725.2.a.z \(2\) \(37.729\) \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-\beta q^{2}+(1+\beta )q^{4}-q^{7}-3q^{8}+3q^{11}+\cdots\)
4725.2.a.ba \(2\) \(37.729\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+q^{4}-q^{7}-\beta q^{8}+\beta q^{11}+\cdots\)
4725.2.a.bb \(2\) \(37.729\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{2}+5q^{4}+q^{7}+3\beta q^{8}+\beta q^{11}+\cdots\)
4725.2.a.bc \(2\) \(37.729\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(1-2\beta )q^{8}+\cdots\)
4725.2.a.bd \(2\) \(37.729\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(1-2\beta )q^{8}+\cdots\)
4725.2.a.be \(2\) \(37.729\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(1-2\beta )q^{8}+\cdots\)
4725.2.a.bf \(2\) \(37.729\) \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q+\beta q^{2}+(1+\beta )q^{4}-q^{7}+3q^{8}-3q^{11}+\cdots\)
4725.2.a.bg \(2\) \(37.729\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{7}+(3+\beta )q^{8}+\cdots\)
4725.2.a.bh \(2\) \(37.729\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{2}+3\beta q^{4}-q^{7}+(1+4\beta )q^{8}+\cdots\)
4725.2.a.bi \(3\) \(37.729\) 3.3.257.1 None \(0\) \(0\) \(0\) \(-3\) \(+\) \(+\) \(+\) \(q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}-q^{7}+(-3+\cdots)q^{8}+\cdots\)
4725.2.a.bj \(3\) \(37.729\) 3.3.257.1 None \(0\) \(0\) \(0\) \(-3\) \(-\) \(+\) \(+\) \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}-q^{7}+(3+\cdots)q^{8}+\cdots\)
4725.2.a.bk \(3\) \(37.729\) 3.3.257.1 None \(0\) \(0\) \(0\) \(3\) \(+\) \(-\) \(-\) \(q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+q^{7}+(-3+\cdots)q^{8}+\cdots\)
4725.2.a.bl \(3\) \(37.729\) 3.3.257.1 None \(0\) \(0\) \(0\) \(3\) \(-\) \(-\) \(-\) \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+q^{7}+(3+\cdots)q^{8}+\cdots\)
4725.2.a.bm \(4\) \(37.729\) 4.4.15529.1 None \(-3\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
4725.2.a.bn \(4\) \(37.729\) 4.4.15529.1 None \(-3\) \(0\) \(0\) \(4\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
4725.2.a.bo \(4\) \(37.729\) 4.4.144344.1 None \(-1\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{7}+(-1-2\beta _{1}+\cdots)q^{8}+\cdots\)
4725.2.a.bp \(4\) \(37.729\) \(\Q(\sqrt{2}, \sqrt{29})\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{7}-2\beta _{1}q^{8}-\beta _{2}q^{11}+\cdots\)
4725.2.a.bq \(4\) \(37.729\) \(\Q(\sqrt{2}, \sqrt{29})\) None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{7}-2\beta _{1}q^{8}+\beta _{2}q^{11}+\cdots\)
4725.2.a.br \(4\) \(37.729\) \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(q+\beta _{3}q^{2}-\beta _{2}q^{4}-q^{7}+(\beta _{1}+\beta _{3})q^{8}+\cdots\)
4725.2.a.bs \(4\) \(37.729\) \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(-\) \(q+\beta _{3}q^{2}-\beta _{2}q^{4}+q^{7}+(\beta _{1}+\beta _{3})q^{8}+\cdots\)
4725.2.a.bt \(4\) \(37.729\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}-q^{7}+2\beta _{2}q^{8}+\cdots\)
4725.2.a.bu \(4\) \(37.729\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}-q^{7}+2\beta _{2}q^{8}+\cdots\)
4725.2.a.bv \(4\) \(37.729\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+q^{7}+2\beta _{2}q^{8}+\cdots\)
4725.2.a.bw \(4\) \(37.729\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+q^{7}+2\beta _{2}q^{8}+\cdots\)
4725.2.a.bx \(4\) \(37.729\) 4.4.144344.1 None \(1\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{7}+(1+2\beta _{1}+\cdots)q^{8}+\cdots\)
4725.2.a.by \(4\) \(37.729\) 4.4.15529.1 None \(3\) \(0\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
4725.2.a.bz \(4\) \(37.729\) 4.4.15529.1 None \(3\) \(0\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
4725.2.a.ca \(5\) \(37.729\) 5.5.2161212.1 None \(0\) \(0\) \(0\) \(-5\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots\)
4725.2.a.cb \(5\) \(37.729\) 5.5.2161212.1 None \(0\) \(0\) \(0\) \(-5\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{7}+(1+\beta _{1}+\cdots)q^{8}+\cdots\)
4725.2.a.cc \(5\) \(37.729\) 5.5.2161212.1 None \(0\) \(0\) \(0\) \(5\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots\)
4725.2.a.cd \(5\) \(37.729\) 5.5.2161212.1 None \(0\) \(0\) \(0\) \(5\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(1+\beta _{1}+\cdots)q^{8}+\cdots\)
4725.2.a.ce \(8\) \(37.729\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(-8\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}-q^{7}+(2\beta _{1}+\beta _{4}+\cdots)q^{8}+\cdots\)
4725.2.a.cf \(8\) \(37.729\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(8\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+q^{7}+(2\beta _{1}+\beta _{4}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4725))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4725)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(675))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(945))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1575))\)\(^{\oplus 2}\)