Properties

Label 5166.2.a
Level $5166$
Weight $2$
Character orbit 5166.a
Rep. character $\chi_{5166}(1,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $55$
Sturm bound $2016$
Trace bound $17$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 5166 = 2 \cdot 3^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5166.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 55 \)
Sturm bound: \(2016\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5166))\).

Total New Old
Modular forms 1024 100 924
Cusp forms 993 100 893
Eisenstein series 31 0 31

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

\(2\)\(3\)\(7\)\(41\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(8\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(38\)
Minus space\(-\)\(62\)

Trace form

\( 100q + 100q^{4} - 8q^{5} + O(q^{10}) \) \( 100q + 100q^{4} - 8q^{5} - 12q^{11} - 4q^{14} + 100q^{16} + 8q^{17} + 8q^{19} - 8q^{20} + 4q^{22} + 124q^{25} + 8q^{26} - 12q^{29} + 8q^{31} - 16q^{34} - 4q^{35} + 24q^{37} - 16q^{38} - 8q^{43} - 12q^{44} - 16q^{46} - 32q^{47} + 100q^{49} - 8q^{50} + 4q^{53} - 4q^{56} + 12q^{58} + 48q^{59} - 24q^{61} - 16q^{62} + 100q^{64} - 40q^{65} + 20q^{67} + 8q^{68} + 4q^{70} + 8q^{71} + 24q^{73} - 16q^{74} + 8q^{76} + 16q^{77} + 32q^{79} - 8q^{80} + 64q^{83} + 40q^{85} + 32q^{86} + 4q^{88} - 32q^{89} + 24q^{91} - 8q^{94} + 64q^{95} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5166))\) 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 41
5166.2.a.a \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(-4\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}+4q^{10}+\cdots\)
5166.2.a.b \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(-4\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}+4q^{10}+\cdots\)
5166.2.a.c \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
5166.2.a.d \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(-2\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
5166.2.a.e \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(-2\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\)
5166.2.a.f \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
5166.2.a.g \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
5166.2.a.h \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
5166.2.a.i \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{11}-6q^{13}+\cdots\)
5166.2.a.j \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-4q^{13}+\cdots\)
5166.2.a.k \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
5166.2.a.l \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
5166.2.a.m \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
5166.2.a.n \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
5166.2.a.o \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
5166.2.a.p \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(2\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
5166.2.a.q \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(3\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+3q^{5}-q^{7}-q^{8}-3q^{10}+\cdots\)
5166.2.a.r \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(3\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
5166.2.a.s \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(4\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots\)
5166.2.a.t \(1\) \(41.251\) \(\Q\) None \(-1\) \(0\) \(4\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+4q^{5}+q^{7}-q^{8}-4q^{10}+\cdots\)
5166.2.a.u \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(-4\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-4q^{10}+\cdots\)
5166.2.a.v \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(-4\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-4q^{10}+\cdots\)
5166.2.a.w \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(-3\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots\)
5166.2.a.x \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(-3\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
5166.2.a.y \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(-3\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
5166.2.a.z \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots\)
5166.2.a.ba \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
5166.2.a.bb \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
5166.2.a.bc \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
5166.2.a.bd \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
5166.2.a.be \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
5166.2.a.bf \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-5q^{11}+4q^{13}+\cdots\)
5166.2.a.bg \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
5166.2.a.bh \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
5166.2.a.bi \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(2\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
5166.2.a.bj \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
5166.2.a.bk \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(2\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\)
5166.2.a.bl \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(3\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}+3q^{10}+\cdots\)
5166.2.a.bm \(1\) \(41.251\) \(\Q\) None \(1\) \(0\) \(3\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
5166.2.a.bn \(2\) \(41.251\) \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-3\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+(-1-\beta )q^{5}+q^{7}-q^{8}+\cdots\)
5166.2.a.bo \(2\) \(41.251\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+(-1+\beta )q^{5}+q^{7}-q^{8}+\cdots\)
5166.2.a.bp \(2\) \(41.251\) \(\Q(\sqrt{33}) \) None \(-2\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
5166.2.a.bq \(2\) \(41.251\) \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(3\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
5166.2.a.br \(2\) \(41.251\) \(\Q(\sqrt{17}) \) None \(2\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
5166.2.a.bs \(2\) \(41.251\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}+q^{8}+\cdots\)
5166.2.a.bt \(3\) \(41.251\) 3.3.568.1 None \(-3\) \(0\) \(-1\) \(-3\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-\beta _{1}q^{5}-q^{7}-q^{8}+\beta _{1}q^{10}+\cdots\)
5166.2.a.bu \(3\) \(41.251\) 3.3.940.1 None \(3\) \(0\) \(-2\) \(-3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}-q^{7}+q^{8}+\cdots\)
5166.2.a.bv \(3\) \(41.251\) 3.3.316.1 None \(3\) \(0\) \(2\) \(3\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+q^{7}+\cdots\)
5166.2.a.bw \(3\) \(41.251\) 3.3.940.1 None \(3\) \(0\) \(3\) \(3\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(1+\beta _{1})q^{5}+q^{7}+q^{8}+\cdots\)
5166.2.a.bx \(4\) \(41.251\) 4.4.11348.1 None \(4\) \(0\) \(-3\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+(-1+\beta _{2}-\beta _{3})q^{5}-q^{7}+\cdots\)
5166.2.a.by \(5\) \(41.251\) 5.5.2620729.1 None \(-5\) \(0\) \(-4\) \(5\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+(-1+\beta _{2})q^{5}+q^{7}-q^{8}+\cdots\)
5166.2.a.bz \(7\) \(41.251\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(0\) \(-4\) \(7\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+q^{7}-q^{8}+\cdots\)
5166.2.a.ca \(7\) \(41.251\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(0\) \(2\) \(-7\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{7}-q^{8}-\beta _{1}q^{10}+\cdots\)
5166.2.a.cb \(7\) \(41.251\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(0\) \(-2\) \(-7\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-\beta _{1}q^{5}-q^{7}+q^{8}-\beta _{1}q^{10}+\cdots\)
5166.2.a.cc \(7\) \(41.251\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(0\) \(4\) \(7\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+(1-\beta _{1})q^{5}+q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5166))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5166)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(123))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(246))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(369))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(574))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(738))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(861))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2583))\)\(^{\oplus 2}\)