Properties

Label 2960.2.a
Level $2960$
Weight $2$
Character orbit 2960.a
Rep. character $\chi_{2960}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $29$
Sturm bound $912$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2960.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 29 \)
Sturm bound: \(912\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2960))\).

Total New Old
Modular forms 468 72 396
Cusp forms 445 72 373
Eisenstein series 23 0 23

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

\(2\)\(5\)\(37\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(-\)\(-\)\(11\)
\(+\)\(-\)\(+\)\(-\)\(11\)
\(+\)\(-\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(10\)
\(-\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(12\)
Plus space\(+\)\(28\)
Minus space\(-\)\(44\)

Trace form

\( 72q + 80q^{9} + O(q^{10}) \) \( 72q + 80q^{9} + 4q^{15} + 8q^{17} + 8q^{19} + 8q^{21} + 12q^{23} + 72q^{25} + 24q^{27} + 8q^{29} + 8q^{31} - 12q^{35} - 8q^{41} - 12q^{43} + 8q^{45} - 24q^{47} + 72q^{49} - 16q^{51} + 16q^{53} + 8q^{55} + 16q^{59} + 24q^{69} - 8q^{71} + 24q^{73} + 48q^{77} - 16q^{79} + 80q^{81} - 16q^{85} + 48q^{87} + 16q^{89} + 64q^{91} - 16q^{93} + 40q^{97} - 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2960))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 37
2960.2.a.a \(1\) \(23.636\) \(\Q\) None \(0\) \(-3\) \(-1\) \(3\) \(-\) \(+\) \(+\) \(q-3q^{3}-q^{5}+3q^{7}+6q^{9}-5q^{11}+\cdots\)
2960.2.a.b \(1\) \(23.636\) \(\Q\) None \(0\) \(-2\) \(1\) \(-3\) \(+\) \(-\) \(-\) \(q-2q^{3}+q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
2960.2.a.c \(1\) \(23.636\) \(\Q\) None \(0\) \(-2\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(q-2q^{3}+q^{5}-q^{7}+q^{9}-3q^{11}-2q^{15}+\cdots\)
2960.2.a.d \(1\) \(23.636\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}-2q^{9}+3q^{11}-4q^{13}+\cdots\)
2960.2.a.e \(1\) \(23.636\) \(\Q\) None \(0\) \(-1\) \(-1\) \(5\) \(-\) \(+\) \(+\) \(q-q^{3}-q^{5}+5q^{7}-2q^{9}-3q^{11}+\cdots\)
2960.2.a.f \(1\) \(23.636\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}-2q^{9}+3q^{11}-q^{15}+\cdots\)
2960.2.a.g \(1\) \(23.636\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q-q^{5}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
2960.2.a.h \(1\) \(23.636\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}-2q^{9}+3q^{11}-6q^{13}+\cdots\)
2960.2.a.i \(1\) \(23.636\) \(\Q\) None \(0\) \(1\) \(1\) \(3\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+3q^{7}-2q^{9}+5q^{11}+\cdots\)
2960.2.a.j \(1\) \(23.636\) \(\Q\) None \(0\) \(2\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(q+2q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots\)
2960.2.a.k \(1\) \(23.636\) \(\Q\) None \(0\) \(2\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(q+2q^{3}-q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots\)
2960.2.a.l \(1\) \(23.636\) \(\Q\) None \(0\) \(2\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(q+2q^{3}+q^{5}-2q^{7}+q^{9}-6q^{13}+\cdots\)
2960.2.a.m \(1\) \(23.636\) \(\Q\) None \(0\) \(2\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(q+2q^{3}+q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots\)
2960.2.a.n \(1\) \(23.636\) \(\Q\) None \(0\) \(3\) \(-1\) \(5\) \(+\) \(+\) \(-\) \(q+3q^{3}-q^{5}+5q^{7}+6q^{9}+3q^{11}+\cdots\)
2960.2.a.o \(2\) \(23.636\) \(\Q(\sqrt{33}) \) None \(0\) \(-4\) \(2\) \(3\) \(-\) \(-\) \(-\) \(q-2q^{3}+q^{5}+(2-\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
2960.2.a.p \(2\) \(23.636\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-6\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{3}+q^{5}+(-3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
2960.2.a.q \(2\) \(23.636\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(6\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{3}+q^{5}+(3-\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
2960.2.a.r \(3\) \(23.636\) 3.3.316.1 None \(0\) \(-1\) \(-3\) \(1\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}-q^{5}+\beta _{1}q^{7}+\beta _{2}q^{9}+(1+\cdots)q^{11}+\cdots\)
2960.2.a.s \(3\) \(23.636\) 3.3.568.1 None \(0\) \(-1\) \(3\) \(1\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+q^{5}+\beta _{1}q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots\)
2960.2.a.t \(3\) \(23.636\) 3.3.148.1 None \(0\) \(0\) \(-3\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta _{2}q^{3}-q^{5}+(-2\beta _{1}+\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
2960.2.a.u \(3\) \(23.636\) 3.3.892.1 None \(0\) \(0\) \(-3\) \(1\) \(-\) \(+\) \(+\) \(q+\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(3+2\beta _{1})q^{9}+\cdots\)
2960.2.a.v \(4\) \(23.636\) 4.4.286164.1 None \(0\) \(-3\) \(4\) \(5\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{3}+q^{5}+(1+\beta _{1})q^{7}+\cdots\)
2960.2.a.w \(5\) \(23.636\) 5.5.973904.1 None \(0\) \(-3\) \(-5\) \(-11\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{3}-q^{5}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
2960.2.a.x \(5\) \(23.636\) 5.5.998068.1 None \(0\) \(-1\) \(-5\) \(2\) \(+\) \(+\) \(+\) \(q-\beta _{4}q^{3}-q^{5}+\beta _{2}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
2960.2.a.y \(5\) \(23.636\) 5.5.6397264.1 None \(0\) \(0\) \(-5\) \(-3\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+\cdots\)
2960.2.a.z \(5\) \(23.636\) 5.5.935504.1 None \(0\) \(1\) \(-5\) \(1\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}-q^{5}-\beta _{3}q^{7}+(\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
2960.2.a.ba \(5\) \(23.636\) 5.5.368464.1 None \(0\) \(1\) \(5\) \(-7\) \(-\) \(-\) \(+\) \(q+\beta _{3}q^{3}+q^{5}+(-1-\beta _{4})q^{7}+(-1+\cdots)q^{9}+\cdots\)
2960.2.a.bb \(5\) \(23.636\) 5.5.583504.1 None \(0\) \(5\) \(5\) \(5\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}+q^{5}+(1+\beta _{2}-\beta _{4})q^{7}+\cdots\)
2960.2.a.bc \(6\) \(23.636\) 6.6.693982032.1 None \(0\) \(-1\) \(6\) \(-8\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{3}+q^{5}+(-1-\beta _{2})q^{7}+(2+\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2960))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2960)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(370))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(592))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(740))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1480))\)\(^{\oplus 2}\)