Properties

Label 3024.2.a
Level $3024$
Weight $2$
Character orbit 3024.a
Rep. character $\chi_{3024}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $39$
Sturm bound $1152$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 39 \)
Sturm bound: \(1152\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3024))\).

Total New Old
Modular forms 612 48 564
Cusp forms 541 48 493
Eisenstein series 71 0 71

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.
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(20\)
Minus space\(-\)\(28\)

Trace form

\( 48 q + O(q^{10}) \) \( 48 q - 8 q^{19} + 48 q^{25} - 8 q^{31} + 32 q^{37} - 16 q^{43} + 48 q^{49} + 8 q^{55} + 48 q^{61} + 56 q^{67} + 24 q^{79} + 40 q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3024))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7
3024.2.a.a \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-4\) \(1\) \(-\) \(+\) \(-\) \(q-4q^{5}+q^{7}-4q^{11}+3q^{13}+7q^{17}+\cdots\)
3024.2.a.b \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-4\) \(1\) \(+\) \(-\) \(-\) \(q-4q^{5}+q^{7}+4q^{11}-q^{13}-3q^{17}+\cdots\)
3024.2.a.c \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-3\) \(-1\) \(-\) \(+\) \(+\) \(q-3q^{5}-q^{7}-3q^{11}-4q^{13}-6q^{17}+\cdots\)
3024.2.a.d \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-3\) \(-1\) \(-\) \(-\) \(+\) \(q-3q^{5}-q^{7}+2q^{13}-3q^{17}+4q^{19}+\cdots\)
3024.2.a.e \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-3\) \(-1\) \(-\) \(+\) \(+\) \(q-3q^{5}-q^{7}+3q^{11}+2q^{13}+6q^{17}+\cdots\)
3024.2.a.f \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-3\) \(-1\) \(-\) \(+\) \(+\) \(q-3q^{5}-q^{7}+6q^{11}-4q^{13}-3q^{17}+\cdots\)
3024.2.a.g \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{5}-q^{7}-6q^{13}+7q^{17}+8q^{19}+\cdots\)
3024.2.a.h \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{5}-q^{7}+3q^{11}-2q^{17}-q^{19}+\cdots\)
3024.2.a.i \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{7}-2q^{11}-4q^{13}+3q^{17}+\cdots\)
3024.2.a.j \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(-\) \(q-q^{5}+q^{7}+q^{11}-4q^{13}+6q^{17}+\cdots\)
3024.2.a.k \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}+2q^{11}-5q^{17}-2q^{19}+\cdots\)
3024.2.a.l \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(-\) \(q-q^{5}+q^{7}+4q^{11}-2q^{13}+3q^{17}+\cdots\)
3024.2.a.m \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(-\) \(q-q^{5}+q^{7}+5q^{11}-2q^{17}+q^{19}+\cdots\)
3024.2.a.n \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{7}+6q^{11}+4q^{13}+3q^{17}+\cdots\)
3024.2.a.o \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{7}+5q^{13}-3q^{17}-2q^{19}-9q^{23}+\cdots\)
3024.2.a.p \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{7}+5q^{13}+3q^{17}-2q^{19}+9q^{23}+\cdots\)
3024.2.a.q \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(q+q^{5}-q^{7}-3q^{11}+2q^{17}-q^{19}+\cdots\)
3024.2.a.r \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(q+q^{5}-q^{7}-6q^{13}-7q^{17}+8q^{19}+\cdots\)
3024.2.a.s \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}-6q^{11}+4q^{13}-3q^{17}+\cdots\)
3024.2.a.t \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}-5q^{11}+2q^{17}+q^{19}+\cdots\)
3024.2.a.u \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(+\) \(-\) \(q+q^{5}+q^{7}-4q^{11}-2q^{13}-3q^{17}+\cdots\)
3024.2.a.v \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}-2q^{11}+5q^{17}-2q^{19}+\cdots\)
3024.2.a.w \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}-q^{11}-4q^{13}-6q^{17}+\cdots\)
3024.2.a.x \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}+2q^{11}-4q^{13}-3q^{17}+\cdots\)
3024.2.a.y \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(3\) \(-1\) \(-\) \(-\) \(+\) \(q+3q^{5}-q^{7}-6q^{11}-4q^{13}+3q^{17}+\cdots\)
3024.2.a.z \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(3\) \(-1\) \(-\) \(+\) \(+\) \(q+3q^{5}-q^{7}-3q^{11}+2q^{13}-6q^{17}+\cdots\)
3024.2.a.ba \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(3\) \(-1\) \(-\) \(+\) \(+\) \(q+3q^{5}-q^{7}+2q^{13}+3q^{17}+4q^{19}+\cdots\)
3024.2.a.bb \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(3\) \(-1\) \(-\) \(+\) \(+\) \(q+3q^{5}-q^{7}+3q^{11}-4q^{13}+6q^{17}+\cdots\)
3024.2.a.bc \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(4\) \(1\) \(+\) \(+\) \(-\) \(q+4q^{5}+q^{7}-4q^{11}-q^{13}+3q^{17}+\cdots\)
3024.2.a.bd \(1\) \(24.147\) \(\Q\) None \(0\) \(0\) \(4\) \(1\) \(-\) \(-\) \(-\) \(q+4q^{5}+q^{7}+4q^{11}+3q^{13}-7q^{17}+\cdots\)
3024.2.a.be \(2\) \(24.147\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-4\) \(-2\) \(+\) \(-\) \(+\) \(q+(-2+\beta )q^{5}-q^{7}+3\beta q^{11}+2\beta q^{13}+\cdots\)
3024.2.a.bf \(2\) \(24.147\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(q-\beta q^{5}-q^{7}+(1+\beta )q^{13}-q^{17}+(-2+\cdots)q^{19}+\cdots\)
3024.2.a.bg \(2\) \(24.147\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+\beta q^{5}-q^{7}+\beta q^{11}+2q^{13}-4\beta q^{17}+\cdots\)
3024.2.a.bh \(2\) \(24.147\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{5}+q^{7}+(-2+\beta )q^{11}+2\beta q^{13}+\cdots\)
3024.2.a.bi \(2\) \(24.147\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q+\beta q^{5}+q^{7}-\beta q^{11}-2q^{13}-7q^{19}+\cdots\)
3024.2.a.bj \(2\) \(24.147\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q-\beta q^{5}+q^{7}-\beta q^{11}+6q^{13}-2\beta q^{17}+\cdots\)
3024.2.a.bk \(2\) \(24.147\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{5}+q^{7}+(2+\beta )q^{11}-2\beta q^{13}+\cdots\)
3024.2.a.bl \(2\) \(24.147\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(1\) \(-2\) \(+\) \(-\) \(+\) \(q+\beta q^{5}-q^{7}+(1+\beta )q^{13}+q^{17}+(-2+\cdots)q^{19}+\cdots\)
3024.2.a.bm \(2\) \(24.147\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(4\) \(-2\) \(+\) \(-\) \(+\) \(q+(2+\beta )q^{5}-q^{7}+3\beta q^{11}-2\beta q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(756))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1512))\)\(^{\oplus 2}\)