Properties

Label 5082.2.a
Level $5082$
Weight $2$
Character orbit 5082.a
Rep. character $\chi_{5082}(1,\cdot)$
Character field $\Q$
Dimension $110$
Newform subspaces $59$
Sturm bound $2112$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 5082 = 2 \cdot 3 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5082.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 59 \)
Sturm bound: \(2112\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5082))\).

Total New Old
Modular forms 1104 110 994
Cusp forms 1009 110 899
Eisenstein series 95 0 95

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

\(2\)\(3\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(8\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(10\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(44\)
Minus space\(-\)\(66\)

Trace form

\( 110 q + 2 q^{2} + 110 q^{4} + 4 q^{5} + 2 q^{8} + 110 q^{9} + O(q^{10}) \) \( 110 q + 2 q^{2} + 110 q^{4} + 4 q^{5} + 2 q^{8} + 110 q^{9} + 4 q^{10} - 12 q^{13} - 8 q^{15} + 110 q^{16} + 4 q^{17} + 2 q^{18} + 4 q^{20} - 2 q^{21} + 114 q^{25} + 4 q^{26} + 28 q^{29} - 8 q^{30} - 32 q^{31} + 2 q^{32} + 4 q^{34} + 8 q^{35} + 110 q^{36} + 4 q^{37} - 8 q^{39} + 4 q^{40} + 20 q^{41} + 2 q^{42} + 4 q^{45} - 8 q^{46} - 16 q^{47} + 110 q^{49} - 2 q^{50} - 8 q^{51} - 12 q^{52} - 4 q^{53} - 24 q^{57} - 4 q^{58} - 8 q^{60} + 4 q^{61} + 110 q^{64} - 8 q^{65} - 24 q^{67} + 4 q^{68} + 2 q^{72} + 4 q^{73} + 28 q^{74} + 8 q^{78} + 48 q^{79} + 4 q^{80} + 110 q^{81} - 12 q^{82} + 16 q^{83} - 2 q^{84} - 8 q^{85} - 8 q^{86} + 36 q^{89} + 4 q^{90} + 8 q^{91} + 8 q^{93} + 16 q^{95} + 20 q^{97} + 2 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5082))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 11
5082.2.a.a \(1\) \(40.580\) \(\Q\) None \(-1\) \(-1\) \(-4\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.b \(1\) \(40.580\) \(\Q\) None \(-1\) \(-1\) \(-4\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.c \(1\) \(40.580\) \(\Q\) None \(-1\) \(-1\) \(-3\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.d \(1\) \(40.580\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.e \(1\) \(40.580\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
5082.2.a.f \(1\) \(40.580\) \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.g \(1\) \(40.580\) \(\Q\) None \(-1\) \(-1\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.h \(1\) \(40.580\) \(\Q\) None \(-1\) \(-1\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.i \(1\) \(40.580\) \(\Q\) None \(-1\) \(-1\) \(4\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.j \(1\) \(40.580\) \(\Q\) None \(-1\) \(1\) \(-3\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.k \(1\) \(40.580\) \(\Q\) None \(-1\) \(1\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.l \(1\) \(40.580\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
5082.2.a.m \(1\) \(40.580\) \(\Q\) None \(-1\) \(1\) \(2\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.n \(1\) \(40.580\) \(\Q\) None \(-1\) \(1\) \(2\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.o \(1\) \(40.580\) \(\Q\) None \(1\) \(-1\) \(-4\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.p \(1\) \(40.580\) \(\Q\) None \(1\) \(-1\) \(-3\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.q \(1\) \(40.580\) \(\Q\) None \(1\) \(-1\) \(-2\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.r \(1\) \(40.580\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
5082.2.a.s \(1\) \(40.580\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
5082.2.a.t \(1\) \(40.580\) \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.u \(1\) \(40.580\) \(\Q\) None \(1\) \(-1\) \(2\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.v \(1\) \(40.580\) \(\Q\) None \(1\) \(-1\) \(2\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.w \(1\) \(40.580\) \(\Q\) None \(1\) \(-1\) \(2\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.x \(1\) \(40.580\) \(\Q\) None \(1\) \(-1\) \(4\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.y \(1\) \(40.580\) \(\Q\) None \(1\) \(1\) \(-3\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.z \(1\) \(40.580\) \(\Q\) None \(1\) \(1\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.ba \(1\) \(40.580\) \(\Q\) None \(1\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
5082.2.a.bb \(1\) \(40.580\) \(\Q\) None \(1\) \(1\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.bc \(2\) \(40.580\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-4\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.bd \(2\) \(40.580\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-3\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.be \(2\) \(40.580\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.bf \(2\) \(40.580\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(1\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.bg \(2\) \(40.580\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(4\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bh \(2\) \(40.580\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(-5\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(-2-\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bi \(2\) \(40.580\) \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(-4\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bj \(2\) \(40.580\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(-1\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.bk \(2\) \(40.580\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bl \(2\) \(40.580\) \(\Q(\sqrt{33}) \) None \(-2\) \(2\) \(3\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bm \(2\) \(40.580\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-4\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.bn \(2\) \(40.580\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-3\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bo \(2\) \(40.580\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(0\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.bp \(2\) \(40.580\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(1\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.bq \(2\) \(40.580\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(4\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.br \(2\) \(40.580\) \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(-5\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-2-\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bs \(2\) \(40.580\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(-4\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bt \(2\) \(40.580\) \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.bu \(2\) \(40.580\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.bv \(2\) \(40.580\) \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(2\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bw \(2\) \(40.580\) \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(3\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bx \(4\) \(40.580\) 4.4.8000.1 None \(-4\) \(-4\) \(2\) \(4\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
5082.2.a.by \(4\) \(40.580\) 4.4.28400.1 None \(-4\) \(-4\) \(4\) \(-4\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}+q^{6}+\cdots\)
5082.2.a.bz \(4\) \(40.580\) \(\Q(\sqrt{3}, \sqrt{5})\) None \(-4\) \(4\) \(0\) \(4\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}-q^{6}+\cdots\)
5082.2.a.ca \(4\) \(40.580\) 4.4.4400.1 None \(-4\) \(4\) \(2\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
5082.2.a.cb \(4\) \(40.580\) 4.4.69264.1 None \(-4\) \(4\) \(4\) \(-4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
5082.2.a.cc \(4\) \(40.580\) 4.4.8000.1 None \(4\) \(-4\) \(2\) \(-4\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
5082.2.a.cd \(4\) \(40.580\) 4.4.28400.1 None \(4\) \(-4\) \(4\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots\)
5082.2.a.ce \(4\) \(40.580\) \(\Q(\sqrt{3}, \sqrt{5})\) None \(4\) \(4\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+q^{6}+\cdots\)
5082.2.a.cf \(4\) \(40.580\) 4.4.4400.1 None \(4\) \(4\) \(2\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
5082.2.a.cg \(4\) \(40.580\) 4.4.69264.1 None \(4\) \(4\) \(4\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5082))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5082)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(847))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1694))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2541))\)\(^{\oplus 2}\)