Properties

Label 2940.2.a
Level $2940$
Weight $2$
Character orbit 2940.a
Rep. character $\chi_{2940}(1,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $20$
Sturm bound $1344$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2940.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(1344\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2940))\).

Total New Old
Modular forms 720 28 692
Cusp forms 625 28 597
Eisenstein series 95 0 95

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

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(-\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(14\)
Minus space\(-\)\(14\)

Trace form

\( 28 q + 28 q^{9} + O(q^{10}) \) \( 28 q + 28 q^{9} - 8 q^{11} - 8 q^{13} - 16 q^{17} - 8 q^{19} + 28 q^{25} - 8 q^{29} + 8 q^{31} - 8 q^{33} - 36 q^{37} - 20 q^{39} - 36 q^{43} + 16 q^{47} - 8 q^{51} + 8 q^{55} - 20 q^{57} + 16 q^{59} - 8 q^{61} - 8 q^{65} - 20 q^{67} - 8 q^{69} + 16 q^{71} + 8 q^{73} - 4 q^{79} + 28 q^{81} + 16 q^{83} + 8 q^{85} + 16 q^{89} - 4 q^{93} + 8 q^{97} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2940))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5 7
2940.2.a.a $1$ $23.476$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $-$ \(q-q^{3}-q^{5}+q^{9}-6q^{11}+q^{15}+6q^{17}+\cdots\)
2940.2.a.b $1$ $23.476$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $+$ \(q-q^{3}-q^{5}+q^{9}-4q^{11}+7q^{13}+\cdots\)
2940.2.a.c $1$ $23.476$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $-$ \(q-q^{3}-q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
2940.2.a.d $1$ $23.476$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $+$ \(q-q^{3}+q^{5}+q^{9}-2q^{11}+q^{13}-q^{15}+\cdots\)
2940.2.a.e $1$ $23.476$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ \(q-q^{3}+q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
2940.2.a.f $1$ $23.476$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ \(q-q^{3}+q^{5}+q^{9}+6q^{11}+4q^{13}+\cdots\)
2940.2.a.g $1$ $23.476$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $-$ \(q+q^{3}-q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\)
2940.2.a.h $1$ $23.476$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $-$ \(q+q^{3}-q^{5}+q^{9}-2q^{11}-q^{13}-q^{15}+\cdots\)
2940.2.a.i $1$ $23.476$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $-$ \(q+q^{3}-q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
2940.2.a.j $1$ $23.476$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $-$ \(q+q^{3}+q^{5}+q^{9}-6q^{11}+q^{15}-6q^{17}+\cdots\)
2940.2.a.k $1$ $23.476$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $-$ \(q+q^{3}+q^{5}+q^{9}-4q^{11}-7q^{13}+\cdots\)
2940.2.a.l $1$ $23.476$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $-$ \(q+q^{3}+q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
2940.2.a.m $2$ $23.476$ \(\Q(\sqrt{7}) \) None \(0\) \(-2\) \(-2\) \(0\) $-$ $+$ $+$ $-$ \(q-q^{3}-q^{5}+q^{9}+(1+\beta )q^{11}-\beta q^{13}+\cdots\)
2940.2.a.n $2$ $23.476$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) $-$ $+$ $+$ $+$ \(q-q^{3}-q^{5}+q^{9}+(2+2\beta )q^{11}+q^{15}+\cdots\)
2940.2.a.o $2$ $23.476$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(0\) $-$ $+$ $-$ $+$ \(q-q^{3}+q^{5}+q^{9}-2q^{11}+2\beta q^{13}+\cdots\)
2940.2.a.p $2$ $23.476$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(0\) $-$ $+$ $-$ $-$ \(q-q^{3}+q^{5}+q^{9}+\beta q^{11}+(1+\beta )q^{13}+\cdots\)
2940.2.a.q $2$ $23.476$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $+$ \(q+q^{3}-q^{5}+q^{9}-2q^{11}-2\beta q^{13}+\cdots\)
2940.2.a.r $2$ $23.476$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $+$ \(q+q^{3}-q^{5}+q^{9}+\beta q^{11}+(-1-\beta )q^{13}+\cdots\)
2940.2.a.s $2$ $23.476$ \(\Q(\sqrt{7}) \) None \(0\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $+$ \(q+q^{3}+q^{5}+q^{9}+(1+\beta )q^{11}+\beta q^{13}+\cdots\)
2940.2.a.t $2$ $23.476$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $+$ \(q+q^{3}+q^{5}+q^{9}+(2+2\beta )q^{11}+q^{15}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2940))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2940)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1470))\)\(^{\oplus 2}\)