Properties

Label 3004.2.a
Level 3004
Weight 2
Character orbit a
Rep. character \(\chi_{3004}(1,\cdot)\)
Character field \(\Q\)
Dimension 62
Newforms 4
Sturm bound 752
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3004 = 2^{2} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3004.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(752\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3004))\).

Total New Old
Modular forms 379 62 317
Cusp forms 374 62 312
Eisenstein series 5 0 5

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

\(2\)\(751\)FrickeDim.
\(-\)\(+\)\(-\)\(31\)
\(-\)\(-\)\(+\)\(31\)
Plus space\(+\)\(31\)
Minus space\(-\)\(31\)

Trace form

\( 62q - 2q^{3} - 2q^{5} + 2q^{7} + 54q^{9} + O(q^{10}) \) \( 62q - 2q^{3} - 2q^{5} + 2q^{7} + 54q^{9} - 2q^{11} - 2q^{13} + 10q^{15} + 2q^{17} - 8q^{19} - 6q^{21} - 2q^{23} + 52q^{25} - 8q^{27} - 4q^{29} + 10q^{31} + 16q^{33} + 8q^{35} - 14q^{37} + 4q^{39} - 6q^{41} + 4q^{43} + 16q^{45} + 6q^{47} + 48q^{49} - 18q^{51} + 8q^{53} + 14q^{55} + 14q^{57} - 10q^{59} - 12q^{61} + 4q^{63} - 10q^{65} - 24q^{67} - 34q^{69} + 16q^{71} + 4q^{73} - 30q^{75} + 2q^{77} + 6q^{79} + 22q^{81} - 4q^{83} - 14q^{85} + 18q^{87} + 2q^{89} - 22q^{91} - 34q^{93} - 24q^{95} - 18q^{97} - 42q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3004))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 751
3004.2.a.a \(1\) \(23.987\) \(\Q\) None \(0\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(q-2q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
3004.2.a.b \(2\) \(23.987\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(6\) \(-\) \(+\) \(q+(1+\beta )q^{3}+(3-\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
3004.2.a.c \(28\) \(23.987\) None \(0\) \(8\) \(11\) \(5\) \(-\) \(+\)
3004.2.a.d \(31\) \(23.987\) None \(0\) \(-10\) \(-11\) \(-7\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(751))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1502))\)\(^{\oplus 2}\)