Properties

Label 4032.2.a
Level 4032
Weight 2
Character orbit a
Rep. character \(\chi_{4032}(1,\cdot)\)
Character field \(\Q\)
Dimension 60
Newforms 50
Sturm bound 1536
Trace bound 13

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.a (trivial)
Character field: \(\Q\)
Newforms: \( 50 \)
Sturm bound: \(1536\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4032))\).

Total New Old
Modular forms 816 60 756
Cusp forms 721 60 661
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.

\(2\)\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(10\)
Plus space\(+\)\(27\)
Minus space\(-\)\(33\)

Trace form

\(60q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(60q \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 52q^{25} \) \(\mathstrut -\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut 60q^{49} \) \(\mathstrut -\mathstrut 56q^{53} \) \(\mathstrut +\mathstrut 32q^{61} \) \(\mathstrut +\mathstrut 8q^{73} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut +\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 8q^{89} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4032))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7
4032.2.a.a \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-4\) \(-1\) \(-\) \(-\) \(+\) \(q-4q^{5}-q^{7}+2q^{17}-2q^{19}+8q^{23}+\cdots\)
4032.2.a.b \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-4\) \(-1\) \(+\) \(-\) \(+\) \(q-4q^{5}-q^{7}+2q^{11}+2q^{13}-4q^{19}+\cdots\)
4032.2.a.c \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-4\) \(1\) \(+\) \(-\) \(-\) \(q-4q^{5}+q^{7}-2q^{11}+2q^{13}+4q^{19}+\cdots\)
4032.2.a.d \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-4\) \(1\) \(+\) \(-\) \(-\) \(q-4q^{5}+q^{7}+2q^{17}+2q^{19}-8q^{23}+\cdots\)
4032.2.a.e \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(q-2q^{5}-q^{7}-4q^{11}-6q^{13}-2q^{17}+\cdots\)
4032.2.a.f \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(q-2q^{5}-q^{7}-4q^{11}+6q^{13}+2q^{17}+\cdots\)
4032.2.a.g \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) \(+\) \(+\) \(+\) \(q-2q^{5}-q^{7}-2q^{11}-2q^{13}+6q^{17}+\cdots\)
4032.2.a.h \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(q-2q^{5}-q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
4032.2.a.i \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) \(-\) \(+\) \(+\) \(q-2q^{5}-q^{7}+6q^{11}+6q^{13}-2q^{17}+\cdots\)
4032.2.a.j \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-2\) \(1\) \(+\) \(+\) \(-\) \(q-2q^{5}+q^{7}-6q^{11}+6q^{13}-2q^{17}+\cdots\)
4032.2.a.k \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{5}+q^{7}-4q^{11}+2q^{13}+6q^{17}+\cdots\)
4032.2.a.l \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(q-2q^{5}+q^{7}+2q^{11}-2q^{13}+6q^{17}+\cdots\)
4032.2.a.m \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{5}+q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
4032.2.a.n \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{5}+q^{7}+4q^{11}+6q^{13}+2q^{17}+\cdots\)
4032.2.a.o \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{7}-4q^{11}-2q^{13}-4q^{17}+4q^{23}+\cdots\)
4032.2.a.p \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{7}-4q^{11}+4q^{13}+2q^{17}+6q^{19}+\cdots\)
4032.2.a.q \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{7}-2q^{11}+2q^{13}-4q^{17}+4q^{19}+\cdots\)
4032.2.a.r \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{7}+4q^{13}-6q^{17}+2q^{19}-5q^{25}+\cdots\)
4032.2.a.s \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{7}+4q^{11}-2q^{13}+4q^{17}-4q^{23}+\cdots\)
4032.2.a.t \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{7}+6q^{11}-2q^{13}-4q^{19}-6q^{23}+\cdots\)
4032.2.a.u \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q+q^{7}-6q^{11}-2q^{13}+4q^{19}+6q^{23}+\cdots\)
4032.2.a.v \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+q^{7}-4q^{11}-2q^{13}+4q^{17}+4q^{23}+\cdots\)
4032.2.a.w \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q+q^{7}+4q^{13}-6q^{17}-2q^{19}-5q^{25}+\cdots\)
4032.2.a.x \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q+q^{7}+2q^{11}+2q^{13}-4q^{17}-4q^{19}+\cdots\)
4032.2.a.y \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+q^{7}+4q^{11}-2q^{13}-4q^{17}-4q^{23}+\cdots\)
4032.2.a.z \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+q^{7}+4q^{11}+4q^{13}+2q^{17}-6q^{19}+\cdots\)
4032.2.a.ba \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(2\) \(-1\) \(-\) \(+\) \(+\) \(q+2q^{5}-q^{7}-6q^{11}+6q^{13}+2q^{17}+\cdots\)
4032.2.a.bb \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(2\) \(-1\) \(+\) \(-\) \(+\) \(q+2q^{5}-q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
4032.2.a.bc \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(q+2q^{5}-q^{7}-6q^{13}+2q^{17}+4q^{19}+\cdots\)
4032.2.a.bd \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(q+2q^{5}-q^{7}-2q^{13}-2q^{17}-4q^{19}+\cdots\)
4032.2.a.be \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(2\) \(-1\) \(+\) \(-\) \(+\) \(q+2q^{5}-q^{7}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
4032.2.a.bf \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(q+2q^{5}-q^{7}+2q^{11}-2q^{13}-6q^{17}+\cdots\)
4032.2.a.bg \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(2\) \(1\) \(-\) \(+\) \(-\) \(q+2q^{5}+q^{7}-2q^{11}-2q^{13}-6q^{17}+\cdots\)
4032.2.a.bh \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(2\) \(1\) \(+\) \(-\) \(-\) \(q+2q^{5}+q^{7}-6q^{13}+2q^{17}-4q^{19}+\cdots\)
4032.2.a.bi \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(2\) \(1\) \(-\) \(-\) \(-\) \(q+2q^{5}+q^{7}-2q^{13}-2q^{17}+4q^{19}+\cdots\)
4032.2.a.bj \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(2\) \(1\) \(-\) \(-\) \(-\) \(q+2q^{5}+q^{7}+2q^{13}-6q^{17}-4q^{19}+\cdots\)
4032.2.a.bk \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(2\) \(1\) \(-\) \(-\) \(-\) \(q+2q^{5}+q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
4032.2.a.bl \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(2\) \(1\) \(+\) \(+\) \(-\) \(q+2q^{5}+q^{7}+6q^{11}+6q^{13}+2q^{17}+\cdots\)
4032.2.a.bm \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(4\) \(-1\) \(+\) \(-\) \(+\) \(q+4q^{5}-q^{7}+2q^{11}+6q^{13}+4q^{17}+\cdots\)
4032.2.a.bn \(1\) \(32.196\) \(\Q\) None \(0\) \(0\) \(4\) \(1\) \(-\) \(-\) \(-\) \(q+4q^{5}+q^{7}-2q^{11}+6q^{13}+4q^{17}+\cdots\)
4032.2.a.bo \(2\) \(32.196\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q+(-1-\beta )q^{5}-q^{7}+(1+\beta )q^{11}-2\beta q^{13}+\cdots\)
4032.2.a.bp \(2\) \(32.196\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(2\) \(+\) \(+\) \(-\) \(q+(-1-\beta )q^{5}+q^{7}+(-1-\beta )q^{11}+\cdots\)
4032.2.a.bq \(2\) \(32.196\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta q^{5}-q^{7}+\beta q^{11}-2q^{13}+\beta q^{17}+\cdots\)
4032.2.a.br \(2\) \(32.196\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+\beta q^{5}-q^{7}+(2-\beta )q^{11}-2q^{13}+\cdots\)
4032.2.a.bs \(2\) \(32.196\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+\beta q^{5}+q^{7}+(-2+\beta )q^{11}-2q^{13}+\cdots\)
4032.2.a.bt \(2\) \(32.196\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{5}+q^{7}-\beta q^{11}-2q^{13}+\beta q^{17}+\cdots\)
4032.2.a.bu \(2\) \(32.196\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) \(+\) \(+\) \(+\) \(q+(1+\beta )q^{5}-q^{7}+(-1-\beta )q^{11}-2\beta q^{13}+\cdots\)
4032.2.a.bv \(2\) \(32.196\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{5}-q^{7}+(2+2\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
4032.2.a.bw \(2\) \(32.196\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(q+(1+\beta )q^{5}+q^{7}+(-2-2\beta )q^{11}+\cdots\)
4032.2.a.bx \(2\) \(32.196\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(2\) \(+\) \(+\) \(-\) \(q+(1+\beta )q^{5}+q^{7}+(1+\beta )q^{11}-2\beta q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4032))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4032)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1344))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2016))\)\(^{\oplus 2}\)