Properties

Label 2100.2.a
Level $2100$
Weight $2$
Character orbit 2100.a
Rep. character $\chi_{2100}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $18$
Sturm bound $960$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(960\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2100))\).

Total New Old
Modular forms 516 18 498
Cusp forms 445 18 427
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.

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(-\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(6\)
Minus space\(-\)\(12\)

Trace form

\( 18 q + 18 q^{9} + O(q^{10}) \) \( 18 q + 18 q^{9} - 4 q^{11} - 4 q^{13} - 12 q^{17} - 2 q^{21} + 4 q^{23} + 28 q^{29} - 8 q^{31} - 12 q^{37} - 8 q^{39} + 28 q^{41} + 8 q^{43} - 8 q^{47} + 18 q^{49} - 4 q^{51} + 12 q^{53} + 8 q^{57} + 32 q^{59} + 44 q^{61} + 16 q^{67} + 4 q^{71} + 20 q^{73} + 8 q^{77} + 16 q^{79} + 18 q^{81} + 32 q^{83} - 8 q^{87} + 36 q^{89} + 16 q^{93} + 20 q^{97} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2100))\) 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
2100.2.a.a $1$ $16.769$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ \(q-q^{3}-q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
2100.2.a.b $1$ $16.769$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ \(q-q^{3}-q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
2100.2.a.c $1$ $16.769$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $-$ $+$ \(q-q^{3}-q^{7}+q^{9}-q^{11}-2q^{13}+6q^{19}+\cdots\)
2100.2.a.d $1$ $16.769$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ \(q-q^{3}-q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
2100.2.a.e $1$ $16.769$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $-$ \(q-q^{3}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
2100.2.a.f $1$ $16.769$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $+$ $+$ $-$ \(q-q^{3}+q^{7}+q^{9}-q^{11}+2q^{13}-8q^{17}+\cdots\)
2100.2.a.g $1$ $16.769$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $-$ \(q-q^{3}+q^{7}+q^{9}+q^{11}+4q^{13}+2q^{17}+\cdots\)
2100.2.a.h $1$ $16.769$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $+$ $+$ $-$ \(q-q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
2100.2.a.i $1$ $16.769$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $-$ \(q-q^{3}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
2100.2.a.j $1$ $16.769$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $-$ $+$ \(q+q^{3}-q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
2100.2.a.k $1$ $16.769$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $+$ \(q+q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
2100.2.a.l $1$ $16.769$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $-$ $+$ \(q+q^{3}-q^{7}+q^{9}-q^{11}-2q^{13}+8q^{17}+\cdots\)
2100.2.a.m $1$ $16.769$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $+$ \(q+q^{3}-q^{7}+q^{9}+q^{11}-4q^{13}-2q^{17}+\cdots\)
2100.2.a.n $1$ $16.769$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $-$ $+$ \(q+q^{3}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
2100.2.a.o $1$ $16.769$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $-$ \(q+q^{3}+q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots\)
2100.2.a.p $1$ $16.769$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $+$ $-$ \(q+q^{3}+q^{7}+q^{9}-q^{11}+2q^{13}+6q^{19}+\cdots\)
2100.2.a.q $1$ $16.769$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $+$ $-$ \(q+q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
2100.2.a.r $1$ $16.769$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $+$ $-$ \(q+q^{3}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2100)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1050))\)\(^{\oplus 2}\)