Properties

Label 3432.2.a
Level $3432$
Weight $2$
Character orbit 3432.a
Rep. character $\chi_{3432}(1,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $24$
Sturm bound $1344$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 3432 = 2^{3} \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3432.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(1344\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3432))\).

Total New Old
Modular forms 688 60 628
Cusp forms 657 60 597
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.

\(2\)\(3\)\(11\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(26\)
Minus space\(-\)\(34\)

Trace form

\( 60q + 60q^{9} + O(q^{10}) \) \( 60q + 60q^{9} + 60q^{25} + 4q^{33} + 32q^{35} + 16q^{37} + 16q^{41} + 32q^{43} + 68q^{49} + 16q^{53} + 48q^{59} - 8q^{67} + 8q^{69} - 16q^{71} + 16q^{73} + 40q^{79} + 60q^{81} + 8q^{87} - 24q^{91} + 8q^{93} - 16q^{95} + 40q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3432))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 11 13
3432.2.a.a \(1\) \(27.405\) \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}-2q^{5}+q^{9}+q^{11}+q^{13}+2q^{15}+\cdots\)
3432.2.a.b \(1\) \(27.405\) \(\Q\) None \(0\) \(-1\) \(-1\) \(3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}-q^{5}+3q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3432.2.a.c \(1\) \(27.405\) \(\Q\) None \(0\) \(-1\) \(0\) \(4\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}+4q^{7}+q^{9}-q^{11}-q^{13}+8q^{17}+\cdots\)
3432.2.a.d \(1\) \(27.405\) \(\Q\) None \(0\) \(1\) \(-3\) \(3\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-3q^{5}+3q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
3432.2.a.e \(1\) \(27.405\) \(\Q\) None \(0\) \(1\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{5}+q^{9}+q^{11}-q^{13}-2q^{15}+\cdots\)
3432.2.a.f \(1\) \(27.405\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{9}+q^{11}-q^{13}-4q^{17}+\cdots\)
3432.2.a.g \(1\) \(27.405\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+2q^{5}+q^{9}-q^{11}+q^{13}+2q^{15}+\cdots\)
3432.2.a.h \(1\) \(27.405\) \(\Q\) None \(0\) \(1\) \(2\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+2q^{5}+4q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
3432.2.a.i \(1\) \(27.405\) \(\Q\) None \(0\) \(1\) \(2\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+4q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3432.2.a.j \(2\) \(27.405\) \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(-4\) \(-4\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+(-2+\beta )q^{5}-2q^{7}+q^{9}+q^{11}+\cdots\)
3432.2.a.k \(2\) \(27.405\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}+(-1-\beta )q^{5}+q^{9}-q^{11}-q^{13}+\cdots\)
3432.2.a.l \(2\) \(27.405\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+(1+\beta )q^{5}+2\beta q^{7}+q^{9}+q^{11}+\cdots\)
3432.2.a.m \(2\) \(27.405\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}+\beta q^{5}-2q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
3432.2.a.n \(3\) \(27.405\) 3.3.404.1 None \(0\) \(3\) \(-4\) \(-6\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+(-1-\beta _{2})q^{5}+(-2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
3432.2.a.o \(3\) \(27.405\) 3.3.892.1 None \(0\) \(3\) \(-1\) \(5\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-\beta _{1}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
3432.2.a.p \(3\) \(27.405\) 3.3.148.1 None \(0\) \(3\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-\beta _{2}q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
3432.2.a.q \(4\) \(27.405\) 4.4.22676.1 None \(0\) \(-4\) \(-3\) \(3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{3})q^{7}+\cdots\)
3432.2.a.r \(4\) \(27.405\) 4.4.70164.1 None \(0\) \(-4\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+\cdots\)
3432.2.a.s \(4\) \(27.405\) 4.4.29268.1 None \(0\) \(-4\) \(4\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+(1-\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
3432.2.a.t \(4\) \(27.405\) 4.4.23252.1 None \(0\) \(-4\) \(4\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+(1+\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+q^{11}+\cdots\)
3432.2.a.u \(4\) \(27.405\) 4.4.70164.1 None \(0\) \(4\) \(1\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+(1+\beta _{2}-\beta _{3})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
3432.2.a.v \(4\) \(27.405\) 4.4.83476.1 None \(0\) \(4\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}+\beta _{3}q^{5}+(-1+\beta _{1}+\beta _{3})q^{7}+\cdots\)
3432.2.a.w \(5\) \(27.405\) 5.5.2172244.1 None \(0\) \(-5\) \(1\) \(-5\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+\beta _{1}q^{5}+(-1-\beta _{4})q^{7}+q^{9}+\cdots\)
3432.2.a.x \(5\) \(27.405\) 5.5.46437524.1 None \(0\) \(5\) \(1\) \(-3\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta _{1}q^{5}+(-1-\beta _{4})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3432))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3432)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(858))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1716))\)\(^{\oplus 2}\)