Properties

Label 6160.2.a
Level $6160$
Weight $2$
Character orbit 6160.a
Rep. character $\chi_{6160}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $51$
Sturm bound $2304$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6160.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 51 \)
Sturm bound: \(2304\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(3\), \(13\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6160))\).

Total New Old
Modular forms 1176 120 1056
Cusp forms 1129 120 1009
Eisenstein series 47 0 47

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

\(2\)\(5\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(56\)
Minus space\(-\)\(64\)

Trace form

\( 120q + 120q^{9} + O(q^{10}) \) \( 120q + 120q^{9} - 8q^{15} - 16q^{19} - 24q^{23} + 120q^{25} - 48q^{27} - 16q^{31} - 48q^{39} + 120q^{49} - 16q^{51} - 48q^{59} + 32q^{61} + 24q^{67} + 32q^{69} + 48q^{71} - 16q^{79} + 120q^{81} + 48q^{83} + 32q^{85} - 48q^{87} - 16q^{89} + 96q^{93} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6160))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 7 11
6160.2.a.a \(1\) \(49.188\) \(\Q\) None \(0\) \(-2\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q-2q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
6160.2.a.b \(1\) \(49.188\) \(\Q\) None \(0\) \(-2\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q-2q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
6160.2.a.c \(1\) \(49.188\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{5}+q^{7}-3q^{9}-q^{11}+2q^{13}+\cdots\)
6160.2.a.d \(1\) \(49.188\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{5}-q^{7}-3q^{9}-q^{11}-6q^{13}+\cdots\)
6160.2.a.e \(1\) \(49.188\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{5}-q^{7}-3q^{9}+q^{11}-6q^{13}+\cdots\)
6160.2.a.f \(1\) \(49.188\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{5}-q^{7}-3q^{9}+q^{11}-2q^{13}+\cdots\)
6160.2.a.g \(1\) \(49.188\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+q^{7}-3q^{9}-q^{11}-6q^{13}+\cdots\)
6160.2.a.h \(1\) \(49.188\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}-3q^{9}+q^{11}+2q^{13}+\cdots\)
6160.2.a.i \(1\) \(49.188\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}-3q^{9}+q^{11}+2q^{13}+\cdots\)
6160.2.a.j \(1\) \(49.188\) \(\Q\) None \(0\) \(2\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+2q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
6160.2.a.k \(1\) \(49.188\) \(\Q\) None \(0\) \(2\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+2q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
6160.2.a.l \(1\) \(49.188\) \(\Q\) None \(0\) \(2\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q+2q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-2q^{15}+\cdots\)
6160.2.a.m \(1\) \(49.188\) \(\Q\) None \(0\) \(2\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+2q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
6160.2.a.n \(1\) \(49.188\) \(\Q\) None \(0\) \(2\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+2q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
6160.2.a.o \(1\) \(49.188\) \(\Q\) None \(0\) \(2\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+2q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
6160.2.a.p \(1\) \(49.188\) \(\Q\) None \(0\) \(2\) \(1\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+2q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+2q^{15}+\cdots\)
6160.2.a.q \(1\) \(49.188\) \(\Q\) None \(0\) \(2\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+2q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
6160.2.a.r \(2\) \(49.188\) \(\Q(\sqrt{33}) \) None \(0\) \(-4\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q-2q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+(1+\cdots)q^{13}+\cdots\)
6160.2.a.s \(2\) \(49.188\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+(-1+\beta )q^{3}-q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
6160.2.a.t \(2\) \(49.188\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+(-1+\beta )q^{3}-q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
6160.2.a.u \(2\) \(49.188\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+(-1+\beta )q^{3}-q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
6160.2.a.v \(2\) \(49.188\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+(-1+\beta )q^{3}+q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
6160.2.a.w \(2\) \(49.188\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}-q^{7}-3q^{9}+q^{11}-\beta q^{13}+\cdots\)
6160.2.a.x \(2\) \(49.188\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q+\beta q^{3}-q^{5}-q^{7}+5q^{9}+q^{11}+(2+\cdots)q^{13}+\cdots\)
6160.2.a.y \(2\) \(49.188\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q+\beta q^{3}-q^{5}+q^{7}-q^{9}-q^{11}+(2+\cdots)q^{13}+\cdots\)
6160.2.a.z \(2\) \(49.188\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+\beta q^{3}-q^{5}+q^{7}-q^{9}+q^{11}+(2+\cdots)q^{13}+\cdots\)
6160.2.a.ba \(2\) \(49.188\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+\beta q^{3}-q^{5}+q^{7}+5q^{9}+q^{11}+2q^{13}+\cdots\)
6160.2.a.bb \(2\) \(49.188\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q+\beta q^{3}+q^{5}-q^{7}-q^{9}+q^{11}+(-2+\cdots)q^{13}+\cdots\)
6160.2.a.bc \(2\) \(49.188\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q+\beta q^{3}+q^{5}+q^{7}-q^{9}-q^{11}+(-2+\cdots)q^{13}+\cdots\)
6160.2.a.bd \(3\) \(49.188\) 3.3.404.1 None \(0\) \(-2\) \(-3\) \(3\) \(+\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{3}-q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
6160.2.a.be \(3\) \(49.188\) 3.3.316.1 None \(0\) \(-2\) \(3\) \(-3\) \(+\) \(-\) \(+\) \(-\) \(q+(-1-\beta _{2})q^{3}+q^{5}-q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6160.2.a.bf \(3\) \(49.188\) 3.3.316.1 None \(0\) \(-2\) \(3\) \(3\) \(-\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{3}+q^{5}+q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6160.2.a.bg \(3\) \(49.188\) 3.3.148.1 None \(0\) \(0\) \(-3\) \(-3\) \(+\) \(+\) \(+\) \(+\) \(q-\beta _{2}q^{3}-q^{5}-q^{7}+(-\beta _{1}-\beta _{2})q^{9}+\cdots\)
6160.2.a.bh \(3\) \(49.188\) 3.3.148.1 None \(0\) \(0\) \(-3\) \(3\) \(-\) \(+\) \(-\) \(+\) \(q-\beta _{2}q^{3}-q^{5}+q^{7}+(-\beta _{1}-\beta _{2})q^{9}+\cdots\)
6160.2.a.bi \(3\) \(49.188\) 3.3.892.1 None \(0\) \(0\) \(-3\) \(3\) \(-\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{3}-q^{5}+q^{7}+(4+\beta _{1}+\beta _{2})q^{9}+\cdots\)
6160.2.a.bj \(3\) \(49.188\) 3.3.148.1 None \(0\) \(0\) \(3\) \(-3\) \(-\) \(-\) \(+\) \(+\) \(q-\beta _{2}q^{3}+q^{5}-q^{7}+(-\beta _{1}-\beta _{2})q^{9}+\cdots\)
6160.2.a.bk \(3\) \(49.188\) 3.3.3028.1 None \(0\) \(0\) \(3\) \(-3\) \(-\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}+q^{5}-q^{7}+(4+\beta _{1}+\beta _{2})q^{9}+\cdots\)
6160.2.a.bl \(3\) \(49.188\) 3.3.564.1 None \(0\) \(2\) \(-3\) \(-3\) \(-\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{3}-q^{5}-q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
6160.2.a.bm \(3\) \(49.188\) 3.3.148.1 None \(0\) \(2\) \(-3\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{3}-q^{5}-q^{7}+(1-\beta _{1}+\beta _{2})q^{9}+\cdots\)
6160.2.a.bn \(3\) \(49.188\) 3.3.148.1 None \(0\) \(2\) \(-3\) \(3\) \(-\) \(+\) \(-\) \(-\) \(q+(1-\beta _{1})q^{3}-q^{5}+q^{7}+(-\beta _{1}+\beta _{2})q^{9}+\cdots\)
6160.2.a.bo \(3\) \(49.188\) 3.3.148.1 None \(0\) \(4\) \(-3\) \(-3\) \(-\) \(+\) \(+\) \(+\) \(q+(1+\beta _{1})q^{3}-q^{5}-q^{7}+(3\beta _{1}+\beta _{2})q^{9}+\cdots\)
6160.2.a.bp \(3\) \(49.188\) 3.3.148.1 None \(0\) \(4\) \(3\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q+(1+\beta _{1})q^{3}+q^{5}-q^{7}+(3\beta _{1}+\beta _{2})q^{9}+\cdots\)
6160.2.a.bq \(4\) \(49.188\) 4.4.25488.1 None \(0\) \(-4\) \(4\) \(4\) \(+\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{3}+q^{5}+q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
6160.2.a.br \(4\) \(49.188\) 4.4.11348.1 None \(0\) \(-2\) \(4\) \(4\) \(-\) \(-\) \(-\) \(-\) \(q+(-1-\beta _{3})q^{3}+q^{5}+q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
6160.2.a.bs \(4\) \(49.188\) 4.4.111028.1 None \(0\) \(0\) \(4\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}+q^{5}+q^{7}+(2+\beta _{2})q^{9}-q^{11}+\cdots\)
6160.2.a.bt \(4\) \(49.188\) 4.4.116404.1 None \(0\) \(0\) \(4\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+q^{5}+q^{7}+(2+\beta _{2})q^{9}+q^{11}+\cdots\)
6160.2.a.bu \(4\) \(49.188\) 4.4.11348.1 None \(0\) \(2\) \(4\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q-\beta _{2}q^{3}+q^{5}+q^{7}+(-\beta _{2}-\beta _{3})q^{9}+\cdots\)
6160.2.a.bv \(5\) \(49.188\) 5.5.8892720.1 None \(0\) \(-2\) \(-5\) \(-5\) \(+\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}-q^{5}-q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6160.2.a.bw \(5\) \(49.188\) 5.5.265504.1 None \(0\) \(-2\) \(-5\) \(5\) \(+\) \(+\) \(-\) \(-\) \(q-\beta _{3}q^{3}-q^{5}+q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
6160.2.a.bx \(5\) \(49.188\) 5.5.15785648.1 None \(0\) \(-2\) \(5\) \(-5\) \(+\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{3}+q^{5}-q^{7}+(3+\beta _{2})q^{9}-q^{11}+\cdots\)
6160.2.a.by \(5\) \(49.188\) 5.5.549616.1 None \(0\) \(2\) \(-5\) \(5\) \(+\) \(+\) \(-\) \(+\) \(q+\beta _{2}q^{3}-q^{5}+q^{7}+(1+\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6160))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6160)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(880))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1232))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1540))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3080))\)\(^{\oplus 2}\)