Properties

Label 2240.2.a
Level $2240$
Weight $2$
Character orbit 2240.a
Rep. character $\chi_{2240}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $38$
Sturm bound $768$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 38 \)
Sturm bound: \(768\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2240))\).

Total New Old
Modular forms 408 48 360
Cusp forms 361 48 313
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.

\(2\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(8\)
Plus space\(+\)\(18\)
Minus space\(-\)\(30\)

Trace form

\( 48q + 48q^{9} + O(q^{10}) \) \( 48q + 48q^{9} + 48q^{25} + 16q^{29} + 32q^{33} + 16q^{37} + 32q^{41} + 48q^{49} + 16q^{53} + 32q^{57} + 32q^{61} + 32q^{69} + 16q^{77} + 80q^{81} + 32q^{85} + 96q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2240))\) 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
2240.2.a.a \(1\) \(17.886\) \(\Q\) None \(0\) \(-3\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(q-3q^{3}-q^{5}-q^{7}+6q^{9}-5q^{11}+\cdots\)
2240.2.a.b \(1\) \(17.886\) \(\Q\) None \(0\) \(-3\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(q-3q^{3}-q^{5}+q^{7}+6q^{9}-3q^{11}+\cdots\)
2240.2.a.c \(1\) \(17.886\) \(\Q\) None \(0\) \(-3\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(q-3q^{3}+q^{5}-q^{7}+6q^{9}+5q^{11}+\cdots\)
2240.2.a.d \(1\) \(17.886\) \(\Q\) None \(0\) \(-3\) \(1\) \(1\) \(+\) \(-\) \(-\) \(q-3q^{3}+q^{5}+q^{7}+6q^{9}-q^{11}+q^{13}+\cdots\)
2240.2.a.e \(1\) \(17.886\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}-2q^{9}-5q^{11}-5q^{13}+\cdots\)
2240.2.a.f \(1\) \(17.886\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}-2q^{9}+3q^{11}+7q^{13}+\cdots\)
2240.2.a.g \(1\) \(17.886\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}-2q^{9}-3q^{11}+q^{13}+\cdots\)
2240.2.a.h \(1\) \(17.886\) \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-q^{7}-2q^{9}+q^{11}-3q^{13}+\cdots\)
2240.2.a.i \(1\) \(17.886\) \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{3}+q^{5}-q^{7}-2q^{9}+q^{11}+q^{13}+\cdots\)
2240.2.a.j \(1\) \(17.886\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}-2q^{9}-5q^{11}-q^{13}+\cdots\)
2240.2.a.k \(1\) \(17.886\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}-2q^{9}+3q^{11}-5q^{13}+\cdots\)
2240.2.a.l \(1\) \(17.886\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}-3q^{9}+2q^{13}+2q^{17}+\cdots\)
2240.2.a.m \(1\) \(17.886\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}-3q^{9}+2q^{13}+2q^{17}+\cdots\)
2240.2.a.n \(1\) \(17.886\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(q+q^{5}-q^{7}-3q^{9}-4q^{11}+6q^{13}+\cdots\)
2240.2.a.o \(1\) \(17.886\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(q+q^{5}-q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots\)
2240.2.a.p \(1\) \(17.886\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}-3q^{9}-4q^{11}-2q^{13}+\cdots\)
2240.2.a.q \(1\) \(17.886\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}-3q^{9}+4q^{11}+6q^{13}+\cdots\)
2240.2.a.r \(1\) \(17.886\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
2240.2.a.s \(1\) \(17.886\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}-2q^{9}-3q^{11}+7q^{13}+\cdots\)
2240.2.a.t \(1\) \(17.886\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}-2q^{9}+5q^{11}-5q^{13}+\cdots\)
2240.2.a.u \(1\) \(17.886\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}-2q^{9}-3q^{11}-5q^{13}+\cdots\)
2240.2.a.v \(1\) \(17.886\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}-2q^{9}+5q^{11}-q^{13}+\cdots\)
2240.2.a.w \(1\) \(17.886\) \(\Q\) None \(0\) \(1\) \(1\) \(1\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{7}-2q^{9}-q^{11}-3q^{13}+\cdots\)
2240.2.a.x \(1\) \(17.886\) \(\Q\) None \(0\) \(1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{7}-2q^{9}-q^{11}+q^{13}+\cdots\)
2240.2.a.y \(1\) \(17.886\) \(\Q\) None \(0\) \(3\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(q+3q^{3}-q^{5}-q^{7}+6q^{9}+3q^{11}+\cdots\)
2240.2.a.z \(1\) \(17.886\) \(\Q\) None \(0\) \(3\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(q+3q^{3}-q^{5}+q^{7}+6q^{9}+5q^{11}+\cdots\)
2240.2.a.ba \(1\) \(17.886\) \(\Q\) None \(0\) \(3\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(q+3q^{3}+q^{5}-q^{7}+6q^{9}+q^{11}+q^{13}+\cdots\)
2240.2.a.bb \(1\) \(17.886\) \(\Q\) None \(0\) \(3\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q+3q^{3}+q^{5}+q^{7}+6q^{9}-5q^{11}+\cdots\)
2240.2.a.bc \(2\) \(17.886\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q-\beta q^{3}-q^{5}-q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)
2240.2.a.bd \(2\) \(17.886\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(q-\beta q^{3}-q^{5}+q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots\)
2240.2.a.be \(2\) \(17.886\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(2\) \(+\) \(+\) \(-\) \(q-\beta q^{3}-q^{5}+q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots\)
2240.2.a.bf \(2\) \(17.886\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(q-\beta q^{3}+q^{5}-q^{7}+(1+\beta )q^{9}+(-4+\cdots)q^{11}+\cdots\)
2240.2.a.bg \(2\) \(17.886\) \(\Q(\sqrt{33}) \) None \(0\) \(-1\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q-\beta q^{3}+q^{5}+q^{7}+(5+\beta )q^{9}+(4-\beta )q^{11}+\cdots\)
2240.2.a.bh \(2\) \(17.886\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q+\beta q^{3}-q^{5}-q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)
2240.2.a.bi \(2\) \(17.886\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta q^{3}-q^{5}-q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)
2240.2.a.bj \(2\) \(17.886\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-2\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{3}-q^{5}+q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots\)
2240.2.a.bk \(2\) \(17.886\) \(\Q(\sqrt{33}) \) None \(0\) \(1\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(q+\beta q^{3}+q^{5}-q^{7}+(5+\beta )q^{9}+(-4+\cdots)q^{11}+\cdots\)
2240.2.a.bl \(2\) \(17.886\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}+(4-\beta )q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2240))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2240)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1120))\)\(^{\oplus 2}\)