Properties

Label 5472.2.a
Level $5472$
Weight $2$
Character orbit 5472.a
Rep. character $\chi_{5472}(1,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $48$
Sturm bound $1920$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5472.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 48 \)
Sturm bound: \(1920\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5472))\).

Total New Old
Modular forms 992 90 902
Cusp forms 929 90 839
Eisenstein series 63 0 63

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

\(2\)\(3\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(15\)
\(+\)\(-\)\(-\)\(+\)\(12\)
\(-\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(42\)
Minus space\(-\)\(48\)

Trace form

\( 90q + 4q^{5} + O(q^{10}) \) \( 90q + 4q^{5} + 4q^{13} - 12q^{17} + 62q^{25} - 12q^{29} + 4q^{37} - 12q^{41} + 74q^{49} + 52q^{53} + 4q^{61} - 24q^{65} - 28q^{73} - 56q^{77} - 16q^{85} + 36q^{89} + 36q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5472))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 19
5472.2.a.a \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(-3\) \(-5\) \(+\) \(-\) \(-\) \(q-3q^{5}-5q^{7}+5q^{11}-4q^{13}+3q^{17}+\cdots\)
5472.2.a.b \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(-3\) \(-3\) \(-\) \(-\) \(+\) \(q-3q^{5}-3q^{7}+3q^{11}-q^{17}-q^{19}+\cdots\)
5472.2.a.c \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(-3\) \(3\) \(+\) \(-\) \(-\) \(q-3q^{5}+3q^{7}-3q^{11}-q^{17}+q^{19}+\cdots\)
5472.2.a.d \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(-3\) \(5\) \(+\) \(-\) \(+\) \(q-3q^{5}+5q^{7}-5q^{11}-4q^{13}+3q^{17}+\cdots\)
5472.2.a.e \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) \(+\) \(+\) \(-\) \(q-2q^{5}-4q^{7}-6q^{11}-4q^{13}+q^{19}+\cdots\)
5472.2.a.f \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) \(+\) \(-\) \(+\) \(q-2q^{5}-4q^{7}-6q^{11}-2q^{13}-6q^{17}+\cdots\)
5472.2.a.g \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(-2\) \(4\) \(-\) \(+\) \(+\) \(q-2q^{5}+4q^{7}+6q^{11}-4q^{13}-q^{19}+\cdots\)
5472.2.a.h \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(-2\) \(4\) \(+\) \(-\) \(-\) \(q-2q^{5}+4q^{7}+6q^{11}-2q^{13}-6q^{17}+\cdots\)
5472.2.a.i \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{7}-2q^{11}-q^{13}-3q^{17}-q^{19}+\cdots\)
5472.2.a.j \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{17}-q^{19}+6q^{23}-5q^{25}-10q^{29}+\cdots\)
5472.2.a.k \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+2q^{17}+q^{19}-6q^{23}-5q^{25}-10q^{29}+\cdots\)
5472.2.a.l \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q+q^{7}+2q^{11}-q^{13}-3q^{17}+q^{19}+\cdots\)
5472.2.a.m \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(q+q^{5}-q^{7}-3q^{11}-4q^{13}+3q^{17}+\cdots\)
5472.2.a.n \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(q+q^{5}-q^{7}-3q^{11}+7q^{17}+q^{19}+\cdots\)
5472.2.a.o \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(q+q^{5}-q^{7}+5q^{11}+4q^{13}+3q^{17}+\cdots\)
5472.2.a.p \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(+\) \(q+q^{5}+q^{7}-5q^{11}+4q^{13}+3q^{17}+\cdots\)
5472.2.a.q \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(+\) \(q+q^{5}+q^{7}+3q^{11}-4q^{13}+3q^{17}+\cdots\)
5472.2.a.r \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(+\) \(q+q^{5}+q^{7}+3q^{11}+7q^{17}-q^{19}+\cdots\)
5472.2.a.s \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(2\) \(-4\) \(+\) \(-\) \(+\) \(q+2q^{5}-4q^{7}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
5472.2.a.t \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(2\) \(-4\) \(-\) \(+\) \(-\) \(q+2q^{5}-4q^{7}+6q^{11}-4q^{13}+q^{19}+\cdots\)
5472.2.a.u \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(2\) \(4\) \(+\) \(+\) \(+\) \(q+2q^{5}+4q^{7}-6q^{11}-4q^{13}-q^{19}+\cdots\)
5472.2.a.v \(1\) \(43.694\) \(\Q\) None \(0\) \(0\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+2q^{5}+4q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
5472.2.a.w \(2\) \(43.694\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+(-1-\beta )q^{5}+2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
5472.2.a.x \(2\) \(43.694\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q+(-1-\beta )q^{5}-2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
5472.2.a.y \(2\) \(43.694\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q+\beta q^{5}+(-1-2\beta )q^{7}+(-2+\beta )q^{11}+\cdots\)
5472.2.a.z \(2\) \(43.694\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta q^{5}+(-1+2\beta )q^{7}+(2+\beta )q^{11}+\cdots\)
5472.2.a.ba \(2\) \(43.694\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q+\beta q^{5}+(1-2\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
5472.2.a.bb \(2\) \(43.694\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{5}+(1+2\beta )q^{7}+(2-\beta )q^{11}+(2+\cdots)q^{13}+\cdots\)
5472.2.a.bc \(2\) \(43.694\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(1\) \(-6\) \(-\) \(-\) \(+\) \(q+\beta q^{5}-3q^{7}+(-2+\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
5472.2.a.bd \(2\) \(43.694\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(q+\beta q^{5}-\beta q^{7}+(-4+\beta )q^{11}-4q^{13}+\cdots\)
5472.2.a.be \(2\) \(43.694\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(+\) \(q+\beta q^{5}+\beta q^{7}+(4-\beta )q^{11}-4q^{13}+\cdots\)
5472.2.a.bf \(2\) \(43.694\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(1\) \(6\) \(-\) \(-\) \(-\) \(q+\beta q^{5}+3q^{7}+(2-\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
5472.2.a.bg \(2\) \(43.694\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(0\) \(+\) \(+\) \(+\) \(q+(1+\beta )q^{5}-2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
5472.2.a.bh \(2\) \(43.694\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q+(1+\beta )q^{5}+2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
5472.2.a.bi \(2\) \(43.694\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-1\) \(+\) \(-\) \(-\) \(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
5472.2.a.bj \(2\) \(43.694\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-1\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{11}+\cdots\)
5472.2.a.bk \(2\) \(43.694\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(1\) \(-\) \(-\) \(+\) \(q+(1+\beta )q^{5}+(1-\beta )q^{7}+(-1-\beta )q^{11}+\cdots\)
5472.2.a.bl \(2\) \(43.694\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(1\) \(-\) \(-\) \(+\) \(q+(1+\beta )q^{5}+(1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
5472.2.a.bm \(3\) \(43.694\) 3.3.229.1 None \(0\) \(0\) \(-5\) \(-1\) \(-\) \(-\) \(-\) \(q+(-2-\beta _{2})q^{5}+\beta _{1}q^{7}-\beta _{1}q^{11}+\cdots\)
5472.2.a.bn \(3\) \(43.694\) 3.3.229.1 None \(0\) \(0\) \(-5\) \(1\) \(-\) \(-\) \(+\) \(q+(-2-\beta _{2})q^{5}-\beta _{1}q^{7}+\beta _{1}q^{11}+\cdots\)
5472.2.a.bo \(3\) \(43.694\) 3.3.469.1 None \(0\) \(0\) \(3\) \(-5\) \(+\) \(-\) \(-\) \(q+(1-\beta _{1})q^{5}+(-2+\beta _{2})q^{7}+(-2+\cdots)q^{11}+\cdots\)
5472.2.a.bp \(3\) \(43.694\) 3.3.469.1 None \(0\) \(0\) \(3\) \(5\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{5}+(2-\beta _{2})q^{7}+(2+\beta _{2})q^{11}+\cdots\)
5472.2.a.bq \(4\) \(43.694\) 4.4.19664.1 None \(0\) \(0\) \(-4\) \(-2\) \(+\) \(+\) \(+\) \(q+(-1+\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+(1+\cdots)q^{11}+\cdots\)
5472.2.a.br \(4\) \(43.694\) 4.4.19664.1 None \(0\) \(0\) \(-4\) \(2\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{3})q^{5}+(1+\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots\)
5472.2.a.bs \(4\) \(43.694\) 4.4.15317.1 None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(-\) \(q+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
5472.2.a.bt \(4\) \(43.694\) 4.4.15317.1 None \(0\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{3}q^{7}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
5472.2.a.bu \(4\) \(43.694\) 4.4.19664.1 None \(0\) \(0\) \(4\) \(-2\) \(-\) \(+\) \(+\) \(q+(1-\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots\)
5472.2.a.bv \(4\) \(43.694\) 4.4.19664.1 None \(0\) \(0\) \(4\) \(2\) \(+\) \(+\) \(-\) \(q+(1-\beta _{3})q^{5}+(1+\beta _{2})q^{7}+(1+\beta _{3})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5472))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5472)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(608))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(684))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1824))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2736))\)\(^{\oplus 2}\)