Properties

Label 900.2.a
Level 900
Weight 2
Character orbit a
Rep. character \(\chi_{900}(1,\cdot)\)
Character field \(\Q\)
Dimension 8
Newform subspaces 8
Sturm bound 360
Trace bound 11

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Defining parameters

Level: \( N \) = \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 900.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(360\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(900))\).

Total New Old
Modular forms 216 8 208
Cusp forms 145 8 137
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.

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

Trace form

\( 8q + 2q^{7} + O(q^{10}) \) \( 8q + 2q^{7} - 4q^{11} - 4q^{13} - 6q^{17} + 6q^{23} + 18q^{29} + 20q^{31} + 8q^{37} + 14q^{41} + 2q^{43} - 6q^{47} - 6q^{53} - 8q^{59} - 8q^{61} + 14q^{67} + 12q^{71} + 8q^{73} - 12q^{79} + 6q^{83} + 26q^{89} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(900))\) 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
900.2.a.a \(1\) \(7.187\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(q-4q^{7}+4q^{11}+4q^{17}+4q^{23}+6q^{29}+\cdots\)
900.2.a.b \(1\) \(7.187\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q-2q^{7}-2q^{13}-6q^{17}-4q^{19}+6q^{23}+\cdots\)
900.2.a.c \(1\) \(7.187\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(q-q^{7}-6q^{11}+5q^{13}+6q^{17}+5q^{19}+\cdots\)
900.2.a.d \(1\) \(7.187\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{7}-7q^{13}-7q^{19}+11q^{31}-10q^{37}+\cdots\)
900.2.a.e \(1\) \(7.187\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q+q^{7}-6q^{11}-5q^{13}-6q^{17}+5q^{19}+\cdots\)
900.2.a.f \(1\) \(7.187\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(-\) \(+\) \(+\) \(q+q^{7}+7q^{13}-7q^{19}+11q^{31}+10q^{37}+\cdots\)
900.2.a.g \(1\) \(7.187\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q+4q^{7}-2q^{13}+8q^{19}-4q^{31}+10q^{37}+\cdots\)
900.2.a.h \(1\) \(7.187\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+4q^{7}+4q^{11}-4q^{17}-4q^{23}+6q^{29}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(900)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 2}\)