Properties

Label 300.2.a
Level 300
Weight 2
Character orbit a
Rep. character \(\chi_{300}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 4
Sturm bound 120
Trace bound 7

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 300.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(300))\).

Total New Old
Modular forms 78 4 74
Cusp forms 43 4 39
Eisenstein series 35 0 35

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

Trace form

\(4q \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 6q^{21} \) \(\mathstrut -\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 6q^{31} \) \(\mathstrut +\mathstrut 10q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 22q^{61} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut +\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(300))\) 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
300.2.a.a \(1\) \(2.396\) \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q-q^{3}-4q^{7}+q^{9}-4q^{11}-4q^{17}+\cdots\)
300.2.a.b \(1\) \(2.396\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(q-q^{3}+q^{7}+q^{9}+6q^{11}-5q^{13}+\cdots\)
300.2.a.c \(1\) \(2.396\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(q+q^{3}-q^{7}+q^{9}+6q^{11}+5q^{13}+\cdots\)
300.2.a.d \(1\) \(2.396\) \(\Q\) None \(0\) \(1\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(300))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(300)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)