Properties

Label 1800.2.a
Level 1800
Weight 2
Character orbit a
Rep. character \(\chi_{1800}(1,\cdot)\)
Character field \(\Q\)
Dimension 24
Newforms 24
Sturm bound 720
Trace bound 13

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Defining parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1800.a (trivial)
Character field: \(\Q\)
Newforms: \( 24 \)
Sturm bound: \(720\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1800))\).

Total New Old
Modular forms 408 24 384
Cusp forms 313 24 289
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.

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(11\)
Minus space\(-\)\(13\)

Trace form

\( 24q - 4q^{7} + O(q^{10}) \) \( 24q - 4q^{7} + 6q^{11} - 4q^{13} - 4q^{17} - 6q^{19} - 12q^{23} - 8q^{29} - 4q^{31} - 4q^{37} - 26q^{41} + 12q^{43} + 20q^{47} + 32q^{49} + 20q^{53} + 32q^{59} + 8q^{61} + 4q^{67} + 32q^{71} + 4q^{73} - 16q^{77} - 12q^{79} - 20q^{83} - 6q^{89} - 32q^{91} + 36q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1800))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5
1800.2.a.a \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(-5\) \(-\) \(-\) \(-\) \(q-5q^{7}+6q^{11}-3q^{13}+2q^{17}+q^{19}+\cdots\)
1800.2.a.b \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q-4q^{7}-4q^{11}+4q^{13}+6q^{17}-4q^{19}+\cdots\)
1800.2.a.c \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(q-4q^{7}+6q^{13}-2q^{17}+4q^{19}-8q^{23}+\cdots\)
1800.2.a.d \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q-4q^{7}+4q^{11}+4q^{13}-6q^{17}-4q^{19}+\cdots\)
1800.2.a.e \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(-3\) \(-\) \(-\) \(+\) \(q-3q^{7}-2q^{11}+3q^{13}+6q^{17}-7q^{19}+\cdots\)
1800.2.a.f \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-2q^{7}-2q^{11}-4q^{13}-2q^{17}+4q^{19}+\cdots\)
1800.2.a.g \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q-2q^{7}-2q^{11}+2q^{13}-6q^{17}+8q^{19}+\cdots\)
1800.2.a.h \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(q-2q^{7}-q^{11}-4q^{13}+5q^{17}+q^{19}+\cdots\)
1800.2.a.i \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-2q^{7}+2q^{11}-4q^{13}+2q^{17}+4q^{19}+\cdots\)
1800.2.a.j \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q-2q^{7}+4q^{11}-4q^{13}-4q^{19}-2q^{23}+\cdots\)
1800.2.a.k \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{7}-4q^{11}+q^{13}+4q^{17}+q^{19}+\cdots\)
1800.2.a.l \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{7}+4q^{11}+q^{13}-4q^{17}+q^{19}+\cdots\)
1800.2.a.m \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q-4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots\)
1800.2.a.n \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+4q^{11}-6q^{13}-6q^{17}-4q^{19}+\cdots\)
1800.2.a.o \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(+\) \(+\) \(q+q^{7}-4q^{11}-q^{13}-4q^{17}+q^{19}+\cdots\)
1800.2.a.p \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(+\) \(+\) \(q+q^{7}+4q^{11}-q^{13}+4q^{17}+q^{19}+\cdots\)
1800.2.a.q \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+2q^{7}-2q^{11}-2q^{13}+6q^{17}+8q^{19}+\cdots\)
1800.2.a.r \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+2q^{7}-q^{11}+4q^{13}-5q^{17}+q^{19}+\cdots\)
1800.2.a.s \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+2q^{7}+4q^{11}+4q^{13}-4q^{19}+2q^{23}+\cdots\)
1800.2.a.t \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(3\) \(+\) \(-\) \(-\) \(q+3q^{7}-2q^{11}-3q^{13}-6q^{17}-7q^{19}+\cdots\)
1800.2.a.u \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(-\) \(q+4q^{7}-4q^{11}-4q^{13}-6q^{17}-4q^{19}+\cdots\)
1800.2.a.v \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q+4q^{7}-4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots\)
1800.2.a.w \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q+4q^{7}+4q^{11}-4q^{13}+6q^{17}-4q^{19}+\cdots\)
1800.2.a.x \(1\) \(14.373\) \(\Q\) None \(0\) \(0\) \(0\) \(5\) \(+\) \(-\) \(+\) \(q+5q^{7}+6q^{11}+3q^{13}-2q^{17}+q^{19}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1800))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1800)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(900))\)\(^{\oplus 2}\)