Properties

Label 468.2.a
Level $468$
Weight $2$
Character orbit 468.a
Rep. character $\chi_{468}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $5$
Sturm bound $168$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 468.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(168\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(468))\).

Total New Old
Modular forms 96 5 91
Cusp forms 73 5 68
Eisenstein series 23 0 23

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

\(2\)\(3\)\(13\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(4\)

Trace form

\( 5q + 2q^{5} + 6q^{7} + O(q^{10}) \) \( 5q + 2q^{5} + 6q^{7} + 6q^{11} - q^{13} - 2q^{17} - 6q^{19} - 8q^{23} + 27q^{25} + 10q^{29} + 10q^{31} - 4q^{35} + 18q^{37} + 10q^{41} - 12q^{43} + 6q^{47} + 9q^{49} - 2q^{53} - 20q^{55} + 6q^{59} - 18q^{61} + 6q^{65} - 14q^{67} - 38q^{71} - 14q^{73} - 12q^{77} - 20q^{79} - 6q^{83} + 4q^{85} + 10q^{89} - 6q^{91} + 4q^{95} + 18q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(468))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 13
468.2.a.a \(1\) \(3.737\) \(\Q\) None \(0\) \(0\) \(-4\) \(4\) \(-\) \(+\) \(+\) \(q-4q^{5}+4q^{7}+4q^{11}-q^{13}+8q^{23}+\cdots\)
468.2.a.b \(1\) \(3.737\) \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(q-2q^{5}-2q^{7}+2q^{11}-q^{13}-6q^{17}+\cdots\)
468.2.a.c \(1\) \(3.737\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+2q^{7}+q^{13}+6q^{17}+2q^{19}-5q^{25}+\cdots\)
468.2.a.d \(1\) \(3.737\) \(\Q\) None \(0\) \(0\) \(4\) \(-2\) \(-\) \(-\) \(-\) \(q+4q^{5}-2q^{7}+4q^{11}+q^{13}-2q^{17}+\cdots\)
468.2.a.e \(1\) \(3.737\) \(\Q\) None \(0\) \(0\) \(4\) \(4\) \(-\) \(+\) \(+\) \(q+4q^{5}+4q^{7}-4q^{11}-q^{13}-8q^{23}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(468))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(468)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 2}\)